Is it possible my account has been hacked?

Hacking would not be my first guess in this situation, but it NEVER hurts to check your security settings on a regular basis.  See the following article about how to re-secure an account that was compromised:  http://gmailaccountrecovery.blogspot.com/  (scroll down to: When you reclaim Your Account).

yes, my filters do send certain messages to trash

One thing to try would be to disable the delete of those filters and see if the problem stops.

and via iphone

This is actually my first guess as to the cause of the problem.  IMAP configuration can be tricky, and it could easily be deleting messages after accessing/downloading them.  Disabling access from your phone for a while might be another good test.