Syncing your email across all devices would require your email account(s?) be IMAP, and not POP3 accounts. IMAP accounts, when read or deleted would be marked as "read" across all devices, and if you delete an email on one device, it's deleted on all devices. So the key is to have those email accounts configured as IMAP when setting them up. (This is the default when setting up most email accounts).
Messages simply require your iPhone be set up to forward SMS messages: Set up iPhone to get SMS messages on Mac - Apple Support
Messages sent to other iPhone users would appear as "blue" in your message thread. Messages sent to non-iPhone users would appear as "green" in your message threads. As long as you're signed in to the same AppleID on all your devices you'll be synchronized across all of them.