3GS crashes right before alarm goes off

My 3GS has a nasty habit to crash right before my alarm goes off.

I often wake up to find my phone has a black screen with a frozen loading circle in it. By holding the power button and the home button I can reset it and it boots up again without a problem.

The strange thing is, it sometimes randomly crashes like this. So I thought it might be a battery issue. But I plug it in at night so when it crashes right before my alarm goes off it has to be something different.
Maybe it's an issue with iOs 5, because this never happened before.

Is there anyone who has a clue what is wrong and what I can do to fix this?

The stock alarm clock that comes with iOs.

Right, a couple of other things arose as problems.

During an alarm the phone would shut off and on. I could see the black screen with the spinning circle as if it would suddenly turn off. Then it would pop right back into iOS and vibrate once.
All the apps I would try to open crash.

When I try to manage my iCloud data (to view and erase backups) the app crashes as well.

Restarting the phone sometimes gives me the connect to iTunes logo. Which will go away after a few dozen more restarts.

All very strange problems that aren't fixed with restoring from a backup even.
Anyone think it's just iOS 5 that messes these things up? Because I've never had any of these problems before.