You and me both sunshine. Exactly the same happened to me, replaced the gamma with an Alpine unit and the remote locking no longer works, you'll probably also notice that the buzzer that tells you you've left your lights on when you open your door no longer works either. It's not much of a problem for me cause i've got an aftermarket CAT1 alarm/immobilizer on it anyway so i still get the remote locking from that but it still annoys me.
I've looked everywhere for an explanation but can't find the answer, i've read of others having the same problem but also loads of people have replaced their head unit (even with Alpine ones) with no problems what so ever.
I was speaking to a guy at a garage last week and he said he thought it was something to do with the fact that all the various systems on the car are linked together and replacing the head unit upsets this - something to do with the stereo having a diagnostics connection? This could all be complete b*ll*cks mind!
I don't know if re-setting the convenience ECU with VAG-COM would do any good? Maybe someone could shed some light on that?
As for your passenger door going crazy - that could be a seperate issue. Does your door lock then unlock immediately? Has the interior light and door light stopped working when you open the door? If so, it's probably the door lock mechanism - common fault on this car. There's a DIY guide on how to fix it on this forum.
If you get the stereo thing sorted or if anyone else knows the answer let me know cause i'm stumped!