Does Maarek get to choose from 3 cards on every crit the enemy ship is dealt while his attack is resolved?

Hypothetical. Land 2 crits. Choose from 3 and deal a Hull Breach. Second crit, choose from 3 and deal a Direct Hit. 3rd crit triggered, choose from 3, etc....

Precisely correct! Whenever the enemy ship would be dealt a face-up damage card when he attacks, he gets to look at the top three and choose. That means, if he manages to land 3 critical damage, he gets to look at three, choose one, then look at the next three, choose one, and so on. Each time, the other damage cards that were NOT selected get discarded (something to take into consideration: those crits probably WON'T affect the remainder of the game, because it's only when a damage deck runs out, that cards are restored to the damage deck).

Obviously, he doesn't get to "look at nine, pick three," in that situation, or look at all the sets of three at the same time (to land the worst possible combo of critical damage cards) - it has to be one at a time. It does mean that any chained damage effects (usually due to some combination of Hull Breach, Fuel Leak, and Direct Hit) could also trigger his ability.

Cool, cheers.

I'd never questioned it before, but earlier, on the table at home, we managed to pick that Hull Breach and chain it into 3 Direct Hits! Kind of made me think....