Not sure this is too big of a deal but what order does one draw and distribute damage cards in regarding regular damage and critical damage?

For example: My ship takes one regular hit and one critical hit. Do I draw one face-down damage card then one face-up damage card or do I first draw the critical face-up damage card then the face-down?

Personally those in my group tend to the former as its a little bit more suspenseful ("You've taken one hit, will the crit be a direct hit and destroy your Tie?!?") and that's just the way we've always been doing it. The cards are always shuffled so the draws are always random. However the situation in parentheses occurred a couple days ago with my Alpha Squadron Pilot taking a hit and a crit, drawing a face-down damage and then drawing the nail in the coffin direct hit from the crit face-up card destroying him. Had I drawn in the opposite order my Interceptor would have lived. That said I wouldn't have drawn the cards any other way but I am curious.

Is this mandated in the rules? Do others operate differently?

You always resolve Hit results before Critical Hit results. It is stated in the rules.

Had I drawn in the opposite order my Interceptor would have lived.

Had the cards been in the opposite order, your ship also would have lived.

There is a correct order, and as StephenEsven says, it's hits before crits. But functionally, there's no difference at all: each draw is a random pull from the cards remaining in the deck.

Resolve [boom/hit] effects one at a time before resolving [kaboom/crit] effects one at a time. Even when Autoblasters are involved you still RESOLVE hits before crits despite being able to cancel the crits but not the hits.

When it comes to actually drawing cards face-down cards are all the same and could be any of the unknown cards in the game. I'd tell you that aside from some minor statistical knowledge you could just replace unknown face-down cards with some kind of token (such as a face-down card!) until such a time that the card is revealed. Cards are also revealed when a ship is killed and this is where someone could gain a small edge by knowing what deck cards have been used although it still doesn't tell you which unknown card will be drawn next.

Awesome, thanks for the clarification.

Cards are also revealed when a ship is killed and this is where someone could gain a small edge by knowing what deck cards have been used although it still doesn't tell you which unknown card will be drawn next.

This I also did not know. Might not be a huge difference knowledge-wise but seeing a bunch of direct hits flipped up on a ship that has been heavily targeted could be somewhat heartening/disheartening.

Awesome, thanks for the clarification.

Cards are also revealed when a ship is killed and this is where someone could gain a small edge by knowing what deck cards have been used although it still doesn't tell you which unknown card will be drawn next.

This I also did not know. Might not be a huge difference knowledge-wise but seeing a bunch of direct hits flipped up on a ship that has been heavily targeted could be somewhat heartening/disheartening.

If they weren't revealed then there would be no point in dealing out all of the damage cards a doomed ship could get immediately before it is destroyed. You shoot at an Academy Pilot with Wedge and have three [booms] that are uncancelled there is really no point to dealling ANY cards to the ship if they are all just going to be set aside face-down. Extra Face-up cards may matter if a ship is sticking around once "destroyed" due to the Simultaneous Fire rules but otherwise there is just a small bit of additional statistical information provided by knowing which cards have been taken out of the damage deck.

Incidentally the damage cards from a destroyed ship are turned up in part to help catch any cheating that may be going on involving a 'stacked' damage deck. Having a ship destroyed and seeing that it had a few face-down Direct Hits on it may be disheartening but seeing that it had three Munitions Failure cards on it is CRIMINAL as there should only be two of them in the entire damage deck.