If a ship is unfortunate enough to be dealt multiple face up damage cards (separate attacks) are the effect of those critical effects cumulative?

For instance if a ship gets two face up Damaged Munitions cards does it remove 2 dice of its choice from attacks; or if a ship gets two face up Power Failure cards is its Engineering value halved and then halved again?

Quite certain you do indeed resolve all the effects of all face-up damage cards when applicable, until the card is either turned face-down, the card is removed, or the ship is destroyed.

Can you imagine a vsd with a engineering of 1...

Yes. All face-up damage cards count, even duplicates.

Makes sense that you'd eventually be damaged to the point where you can't repair yourself anymore. Really sucks, but them's the breaks.

Guess it would depend on the wording of the critical effect.

If for example one says the printed engineering value on a card is halved, two identical ones of those wouldn't stack.

If it says when doing an engineering command half the amount you receive then yes thoses would stack. Don't have any cards to hand so couldn't say what it actually says.