Wizkids Rules!

Can you spend evade tokens against attacks that do not allow you to roll defense dice like Borg Missile?

Attack: Disable this card to perform this attack.
The target ship does not sustain normal damage from this attack. Instead, place 1 Auxiliary Power Token beside the target ship AND destroy one of its Active Shields for each [hit] or [crit] result. The target ship does not roll defense dice against this attack. This Upgrade may only be purchased for a Borg ship.

Yes. Cards that state "does not/do not roll defense dice" only modify the number of dice that are rolled, they do not skip or cancel that step of attacking or defending. Evade tokens may be spent during the modify defense dice step of combat.

Does Borg Missile give an aux token for every hit or crit result or is it a max of just 1 aux token?

Borg Missile gives you 1 auxiliary token if any hits or critical hits are rolled (and not canceled) when you are making an attack with it.

This will be added to the FAQ.