1) Something is wrong with the phone. It's under warranty. Have it replaced.
2) If th calendar was
Google Calendar, it'll sync if Calendar sync is enabled in the Google (not gmail) account. (Google contacts - but not Phone, Device or SIM contacts - are also backed up, as are any of your pictures is you have picture sync enabled.)
Photos, notes, etc., if they weren't backed up, are gone. The phone has to be rooted to recover deleted files, assuming they were deleted, and your data partition wasn't just wiped. (And that voids the warranty.)
This is one reason you should have
anything you don't want to lose backed up to at least 2 separate destinations. There's no guarantee that the phone won't suddenly go bad, drop into water or get run over by a truck.