>Also, does the luck stat affect any of the following things:
>Skill learning speed
>Fleeing successfully
>Teleporting into aggro mobs
>Escaping quicksand

None of the above.

Here's the full list:

1) It has a small effect on saves (to give you some idea, INT and WIS each have as big or greater effect).

2) Various combat skills where you see some kind of 'critical success' echo, generally with 'luck' somewhere in it. Pincer, charge, etc.

3) Gambling.