Does each transport use an individual deck, or would they share one? I didn't see it in the rule book. My instinct is each one uses its own deck.

Each ship comes with its own damage decks. Use one pair of decks for each ship until FFG rules otherwise.

Page 4 of the Transport rules insert:

The GR-75 has two unique Damage decks: one for the ships fore section, and one for the ships aft section.

I believe each ship has it's own damage deck. We know that the damage deck is different for the CR-90, so clearly you would not use one deck for the two different craft. Finally, in the Epic Tournament Rules, page 4, we find a bit of clarification. Section 3 in Epic Team Play Deployment Procedures.

• Each team captain shuffles his core set Damage deck and any Huge ship damage decks thoroughly and presents them to the opposing team’s captain. The opposing captain may shuffle and cut each deck if desired

Similar text appears in the Epic Dogfight deployment rules. I'm fairly certain this means that, if you have two Transports, each has their own deck.

I do think that you use two decks per ship. And I hope FFG addresses this issue in the next FAQ.

Playing devil's advocate: A huge ship comes with two damage decks. The plural form may refer to that and not to several ships.

I do think that you use two decks per ship. And I hope FFG addresses this issue in the next FAQ.

Playing devil's advocate: A huge ship comes with two damage decks. The plural form may refer to that and not to several ships.

And that may be contributing to the confusion around how many decks.

Slightly related question that I may be missing in the rule book: Do you have to destroy one or both sections of a huge ship to count it as killed?

You use individual decks for each ship. There are only 10 cards in each section of the damage deck, and with the refit, it can have 10 hull. Which means that all 10 might be dealt from a single deck. Which means that each ship needs its unique set of decks.

Slightly related question that I may be missing in the rule book: Do you have to destroy one or both sections of a huge ship to count it as killed?

The transport doesn't track damage to its 2 sections separately, it's all one big pool of damage, so when the total damage cards from both decks equals it's hull value, the whole ship is destroyed.

The corvette on the other hand DOES keep the damage separate. When one of its sections is "destroyed" you flip the card for it over to the "crippled" side which has reduced stats and abilities, but the ship is still in the game. To fully destroy the corvette you have to destroy both sections independently.