Vinto's Rapid Fire ability allows him to re-roll all dice when he is the attacker. I assume this means that he can't just re-roll one or two, but has to re-roll all?

What happens if a die has been re-rolled already? For example if he uses Diala's ability to re-roll one die as he's only unhappy with one, but the result isn't satisfactory, can he then use Rapid Fire to re-roll the remaining dice?

Yes, it is all or none.

Except if some of them have already been rerolled; then those dice cannot be rerolled by another ability (but I assume the ability can still be used to reroll the other dice).

All dice (attack and defense) that have not yet been rerolled in the same attack will get rerolled with Rapid Fire, if Vinto chooses to use the ability.

You could argue that the card only lets you reroll all dice, so if you can't reroll all dice then you can't use the card at all.

You could, but it would not take you far.

There is not a single ability in the game that would have hidden (unwritten) pre-requisites. You need the trigger, and you need to pay the associated costs to activate an ability. When you resolve an ability, you perform the parts you can and ignore the parts you cannot perform.