You can use abilities anytime you want.
Except in the middle of resolving another card. E.g. "Exchange 2" - you cannot exchange card X to get a new card Y, use card Y's ability, then exchange card Y.
PS: OP, here is the rule for your question:
After drawing each fighting card you can always decide to use the special ability of any drawn faceup
fighting card (regardless of left or right cards) in any order you like. You can use each special ability
only once during the fight against the hazard and turn the chosen card 90°. Only after using the ability
completely, you can activate the next ability of another card (see special abilities on page 10).