#1
Is this normal or should I really try hard to work against it? The higher up the neck I start to play the more I have to point my thumb towards the headstock, otherwise my thumb goes comletely sideways and bent.
#2
I'd say thats normal. When you get higher up the neck, you tend to be playing lead, so you grip the neck differently. It's not comfortable to be able to keep your thumb perpendicular to the neck while playing lead, or atleast I don't think so. However, barre chords, or just chords in general, my thumb tends not to face the headstock too much.

If it's not uncomfortable for you, then it's probably ideal. Guitar playing has guide lines, but not rules, remember that.
#3
Sounds kinda normal too me. As long as you are comfortable and playing up to your ability that way, thats fine.
top axes:
Taylor GS8
Fender American Strat (w/DiMarzio pickups)
Epiphone Les Paul
#5
Eh? It's the opposite way for me. When I'm playing chords I'm more relaxed so my thumb tends to be parallel to the neck. For lead I need it perpendicular because I find it means I can reach all the strings/frets better.
I suppose if you don't find you have any problems playing the way you do then it's fine, but if you're struggling with reaching strings/frets try to make your thumb more perpendicular to the neck and make sure you bend your wrist.