Iphone back from repair, problems with Google Sync

I just got back a "new" iPhone from apple as the one I bought had some hardware problems.

Leaving behind the fact that before sending it I made a backup on iCloud (it said successful) which I wasn't able to find today, as I started restore I soon realized that a few things weren't right.

First of all the iPhone came up with a strange and unknown apple account email, asking me for its password (and sometimes it still shows up), but the most important thing is that no matter what I do I no longer am able to sync my emails, my contacts and my calendar through Google Sync and exchange.

I tried deleting my account, I tried re-setting it, I even tried a new password but no luck, even though the test that iOS does is all okey.

It says no error, besides "unable to connect to the server" when I try to access my mails.

Thank you!