Is there a specific time when the heros can use their fatigue points. I know it's only during their turn, but when during their turn? Can they use it for adding movement points at activation before getting the effect of a rest order per exemple?

the rest order is finished at the start of the hero turn so you would have all your fatigue back before you needed to spend fatigue anyway.

But can you add movement Points with the remaining fatigue before activating the rest order to full your fatigue back?

JitD Rulebook p. 8

Heroe Player's Turn
Step 1: Refresh cards
Step 2: Equip items
Step 3: Take an action (A hero is not allowed to do anything except refresh and equip before he declares the action he is taking.)

I interpret it this way:

Heroe Player's Turn
Step 1: Refresh cards ( Start of Turn , where multiple things can take place, refreshing Cards, ending of Orders like "Rest" and effects of well... Effectmarkers)

Step 2: Equip items (Choose Equipment)

Step 3: Take an action (Choose "Advance" "Run" or "Ready")

From this point (after you have chosen your action!) you can use Movementpoints to drink Potions, use fatigue for adding movemenpoints or additional dice in battles etc.

Also this might be helpful for Step 1:

Descent FAQ p. 6

Q: What is the proper timing of events that occur “at the
beginning of a player’s turn”?
A: When multiple events may occur “at the beginning of a
player’s turn,” such as a hero affected by multiple different
status effects like Burn and Bleed, that player may decide
in which order to resolve them. The player must resolve
all “start of turn” effects before proceeding with the rest of
his turn.

So no, you can't use all you remaining Fatigue for Movementpoint at the Start of your turn before using your Rest-Order to regain all fatigue.

Thanks for the quick and precise answer!

One other useful rules citation:

"A hero is not allowed to do anything except refresh and equip before he declares the action he is taking." (p.8, under "Step 3: Take an Action")

Therefore, unless otherwise stated, anything that a hero can do "during his turn" can only be done after he declares his action. This includes spending fatigue.