Can a hero move by spending fatigue without a move action? Can he do this more than once a turn?
Yes, fatigue tokens may be used as often as you like to gain movement points. These movement points are spent just like regular movement points, to perform Movement Actions or to move (gold chart page 16 shows examples).
From the rule book (page 18):
Spending Fatigue for Movement - At any time during a hero’s turn, he may spend one fatigue to gain one movement point, even if he is currently taking the battle action. This may be done as often as the hero desires. Movement points gained in this manner are spent just like normal movement points
Yes, to both questions. One fatigue for one movement.