Please find bellow, logs i feel be interesting. May be the latest one regarding duplicate account i suspect on apple id's servers.
One element more maybe, each time i start up a e-Device, the system ask to enter my iCloud password. That was not the case before my issue.
30/11/2015 08:37:07,774 imagent[399]: [Warning] IMDAccountController: Could not find an account for service: (null)
30/11/2015 08:37:07,775 imagent[399]: [Warning] IMDAccountController: Could not find an account for service: (null)
30/11/2015 08:37:07,780 imagent[399]: [Warning] SMSServiceSession: Error no IDS Service available for SMS Relay
30/11/2015 08:37:07,780 imagent[399]: [Warning] SMSServiceSession: Error no IDS Service available for SMS Relay
30/11/2015 08:37:07,780 imagent[399]: [Warning] SMSServiceSession: Error no IDS Service available for SMS Relay
30/11/2015 08:37:07,780 imagent[399]: [Warning] SMSServiceSession: Error no IDS Service available for SMS Relay
30/11/2015 08:37:07,791 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,791 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,805 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,805 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,808 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,808 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 1
30/11/2015 08:37:07,841 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:07,841 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:07,854 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:07,854 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:08,876 accountsd[327]: [Warning] Unhandled server key: alert
30/11/2015 08:37:08,905 accountsd[327]: [Warning] Unhandled server key: alert
30/11/2015 08:37:08,930 accountsd[327]: [Warning] Unhandled server key: alert
30/11/2015 08:37:08,955 accountsd[327]: [Warning] Unhandled server key: alert
30/11/2015 08:37:09,021 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,044 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,069 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,095 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,108 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,208 accountsd[327]: AIDA Notification plugin running
30/11/2015 08:37:09,883 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:09,883 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 2
30/11/2015 08:37:12,211 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,211 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,211 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,211 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,224 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,224 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,238 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,239 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,251 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,251 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,266 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,266 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,282 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,282 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,297 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,297 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 3
30/11/2015 08:37:12,301 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:12,301 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:12,315 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:12,315 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:13,959 secd[356]: __SOSCCProcessSyncWithAllPeers_Server_block_invoke sync with all peers failed: Error Domain=com.apple.security.sos.error Code=1032 "peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found" UserInfo={NSDescription=peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found}
30/11/2015 08:37:13,960 CloudKeychainProxy[454]: __39-[UbiqitousKVSProxy doSyncWithAllPeers]_block_invoke_2 <UB--s--C---> syncWithAllPeers (null), rescheduling timer
30/11/2015 08:37:14,283 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:14,283 Messages[688]: [Warning] (IMAccount: 0x7f9672c139c0 [ID: B1657148-B519-4C8C-B28F-3A98694588D9 Service: IMService[iMessage] Login: E:myaccount@icloud.com Active: YES LoginStatus: Connecté]) - isActive: YES - isOperational: NO - registration status: 4
30/11/2015 08:37:14,410 accountsd[327]: [AOSAccounts] : [iCloudIDNotificationPlugin] -[iCloudIDNotificationPlugin canSaveAccount:inStore:] : Returning false. Same DSID found. Found duplicate for account myaccount@me.com (52F6E70D-03C5-4C6A-95E9-D5DE7BEDC114) which is myaccount@icloud.com (66280174-CFA9-4275-B664-7CE1CF4CA992)
30/11/2015 08:37:14,410 accountsd[327]: [AOSAccounts] : [iCloudIDNotificationPlugin] -[iCloudIDNotificationPlugin canSaveAccount:inStore:] : Returning 0 account myaccount@me.com (52F6E70D-03C5-4C6A-95E9-D5DE7BEDC114) clientbundleID : com.apple.accountSync
30/11/2015 08:37:17,952 identityservicesd[331]: <IMMacNotificationCenterManager: 0x7f82ab938ef0>: NC Disabled: NO
30/11/2015 08:37:17,955 identityservicesd[331]: <IMMacNotificationCenterManager: 0x7f82ab938ef0>: DND Enabled: NO
30/11/2015 08:37:17,955 identityservicesd[331]: <IMMacNotificationCenterManager: 0x7f82ab938ef0>: Updating enabled: YES (Topics: (
"com.apple.private.alloy.icloudpairing",
"com.apple.private.alloy.continuity.encryption",
"com.apple.private.alloy.continuity.activity",
"com.apple.madrid",
"com.apple.private.ids",
"com.apple.private.alloy.phonecontinuity",
"com.apple.private.alloy.phone.auth",
"com.apple.private.alloy.keychainsync",
"com.apple.private.alloy.fmf",
"com.apple.private.alloy.sms",
"com.apple.private.alloy.thumper.keys",
"com.apple.private.alloy.maps",
"com.apple.private.alloy.screensharing",
"com.apple.private.alloy.continuity.tethering"
))
30/11/2015 08:37:18,454 blued[90]: ***** Removing all cloud paired devices
30/11/2015 08:37:29,204 secd[356]: __SOSCCProcessSyncWithAllPeers_Server_block_invoke sync with all peers failed: Error Domain=com.apple.security.sos.error Code=1032 "peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found" UserInfo={NSDescription=peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found}
30/11/2015 08:37:29,205 CloudKeychainProxy[454]: __39-[UbiqitousKVSProxy doSyncWithAllPeers]_block_invoke_2 <UB--s--C---> syncWithAllPeers (null), rescheduling timer
30/11/2015 08:37:38,729 com.apple.spotlight.IndexAgent[565]: [com.apple.corespotlight.log] Not allowed to pass in bundle ID
30/11/2015 08:37:38,730 IMDPersistenceAgent[414]: [com.apple.corespotlight.log.index] Finished "index items"(6) with error:Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:38,730 IMDPersistenceAgent[414]: [Warning] IMDChatAddMessageToSpotlight: indexing searchable items failed with error Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:38,730 IMDPersistenceAgent[414]: [Warning] IMDChatAddMessageToSpotlight: indexing searchable items failed with error Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:39,743 identityservicesd[331]: [Warning] Warning, missing mailto:contact-iMessage_Account@icloud.com in (null)
30/11/2015 08:37:39,743 identityservicesd[331]: [Warning] Warning, missing tel:+33695308408 in (null)
30/11/2015 08:37:39,756 com.apple.spotlight.IndexAgent[565]: [com.apple.corespotlight.log] Not allowed to pass in bundle ID
30/11/2015 08:37:39,756 IMDPersistenceAgent[414]: [com.apple.corespotlight.log.index] Finished "index items"(8) with error:Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:39,756 IMDPersistenceAgent[414]: [Warning] IMDChatAddMessageToSpotlight: indexing searchable items failed with error Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:39,756 IMDPersistenceAgent[414]: [Warning] IMDChatAddMessageToSpotlight: indexing searchable items failed with error Error Domain=CSIndexErrorDomain Code=-1003 "(null)"
30/11/2015 08:37:44,209 secd[356]: __SOSCCProcessSyncWithAllPeers_Server_block_invoke sync with all peers failed: Error Domain=com.apple.security.sos.error Code=1032 "peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found" UserInfo={NSDescription=peer: pTYhrODY2SQZOU8JV9FYMUUBhs not found}
30/11/2015 08:37:44,210 CloudKeychainProxy[454]: __39-[UbiqitousKVSProxy doSyncWithAllPeers]_block_invoke_2 <UB--s--C---> syncWithAllPeers (null), rescheduling timer
30/11/2015 08:37:14,410 accountsd[327]: [AOSAccounts] : [iCloudIDNotificationPlugin] -[iCloudIDNotificationPlugin canSaveAccount:inStore:] : Returning false. Same DSID found. Found duplicate for account myaccount@me.com (52F6E70D-03C5-4C6A-95E9-D5DE7BEDC114) which is myaccount@icloud.com (66280174-CFA9-4275-B664-7CE1CF4CA992)
30/11/2015 08:37:14,410 accountsd[327]: [AOSAccounts] : [iCloudIDNotificationPlugin] -[iCloudIDNotificationPlugin canSaveAccount:inStore:] : Returning 0 account myaccount@me.com (52F6E70D-03C5-4C6A-95E9-D5DE7BEDC114) clientbundleID : com.apple.accountSync