I suggest to use IMAP on all devices and no Exchange
I am using my mailaccounts (all IMAP) on PC, Mac, Android- & iOS-devices
in fact, my accounts are Gmail.com, Telenet.be & icloud.com
On my PC I utilise Microsoft Office Outlook 2013 with the 3 mailaccounts installed as IMAP
On my Mac mini I utilise Mail provided by the OS (Mavericks) with the 3 mailaccounts installed as IMAP
On my Ipad (1) I utilise Mail provided by the iOS 5.1.1 with the 3 mailaccounts installed as IMAP
On my Android 4.1 pad I utilise Gmail with the 3 mailaccounts installed as IMAP
On my Nexus4 phone I utilise Gmail with the 3 mailaccounts installed as IMAP
As Calendar I have Google synchronised with the Mavericks calendar on my mac mini
All works perfect together
Rik