If a ship has 4 hull and has 0 shields and the enemy shoots doing 5 or more damage, do I continue taking damage cards even though only 4 were needed to kill my ship? In xwing you do this. Also, if I have a zombie ship with a crit card and I do a repair, can I get rid of the crit effect. I understand I can't heal the ship cause he is already dead at end of round.

Its not explicitly stated wether you draw the additional cards above or not. I'd wager, based on a forthcoming rules quote, that immediately means immediately and that maens you draw your damage up to your hull value, then you're immediately destroyed.

As for the second, again, Rieekan questions are awaiting to be answered in Bulk by FFG...

Most - but not all - have argued thusfar that you're going to be destroyed, as your destroyed trigger has gone off , even if you subsequently repair... HOWEVER< if you are just talking about Repairing a Crit, so you don't suffer that crit during your activation , you can totally do that... That might get rid of your inability to target at long range, for example...

I remember something like "a ship cannot have assigned more damage cards than its hull value" but I am not sure and I don't have the rule book right now.

Here's your Quote ( italic emphasis mine):

(RRG, Page 4, Damage)

Damage

Ships and squadrons can suffer damage from attacks, obstacles, and other game effects.

• When a ship suffers damage, it suffers that damage one point at a time . For each point, reduce the shields in the defending hull zone by one. If the defending hull zone has no shields to lose, deal a facedown damage card to the ship instead.

• When a ship has damage cards equal to its hull value , it is immediately destroyed .

• Damage cards are dealt one at a time.

So the only time you might keep drawing Damage cards, is in the case of a Rieekan Zombie ship. And mostly because you could load it up with Critical Damage Faceup Cards in order to really limit its one remaining potential activation.

I was wondering about that since I keep seeing people drawing damage cards beyond the hull value (which I understand now to be how it's done in X-wing).

So I looked it up and found what Drasnighta quoted, but you can also find on page 5 :

Destroyed Ships and Squadrons : A ship is destroyed when it has damage cards equaling or exceeding its hull value.

...but you can also find on page 5 :

Destroyed Ships and Squadrons : A ship is destroyed when it has damage cards equaling or exceeding its hull value.

The "or exceeding" clause is because you could end up with more damage cards than hull value if your hull value is somehow reduced. For example, if a VSD has 9 damage cards when Admiral Motti's ship gets destroyed.

When taking damage from an attack, you stop drawing cards as soon as the ship is destroyed, as Dras said.