"Best Position" doesn't affect how they will play if they don't play in that position. You can play him anywhere you like with no penalty - it's just where the programmers think he will play best based on his skills. However, I have some players that seem to play just as well in any position. It seems that PF and C are pretty similar, actually.
To answer your first question, no I don't believe it is fixed. I swear that after a training "pop" a couple of my players changed their best position.
Friends Do not Let Friends Play 2-3 Zone