Can you use fatigue to move after your second action or is your turn over after the second action (e.g. Could I fatigue move, use a move action, use a rest action, then fatigue move)?
You could but only if you have enough fatigue left, the rest restores your fatigue at the end of your turn.
But you could use two action then fatigue move.
Does High Mage Quellen's hero ability allow him to remove fatigue from other players or only himself?
It says "you" recover, so only quellen
Can hero #3 hit both dragons with a melee attack or only the white dragon (#1)?
If the red dragon (#2) wasnt there could hero #3 move to the #2 space by going between the wall and the white dragon (#1)
If hero #3 wasnt there could hero #4 hit the red dragon (#2) with a ranged attack?
yes. though a wildlander with eagle eyes could attack as is.