So, if hypothetically Backdraft has a large ship caught in both its primary and auxillary arc, can it add a critical hit on both of its attacks? I ask because his ability reads, "when attacking ship inside your auxillary firing arc, you may add 1 critical result". In this scenario, the large ship IS inside Backdraft's auxillary arc, even when he is firing out his primary arc. Thank you

Yes, he adds a crit on both attacks

Backdraft's ability does not care about which arc the attack is coming out of only where the defender is in relation to his back arc. In the rare situation where the defender is in the back arc and front arc at the same time backdraft's ability will work on both shots (and it feels fantastic when it happens)