Timo, perhaps you can confirm this asap.
I started with both expansions straight away because I wanted to use the new battle rules in preference to reading the old ones.
Page 9 in Pilot Academy shows the red, yellow and amber symbols for gaining extra cards from improvements into your battle deck. I've just realised that these should be attack, defence and support symbols that appear as well as the red/yellow/amber that are on the new captain/ship cards.
We couldn't understand why we received only a few cards for 6 rounds of combat.
Players who have used the original battle system will probably realise this straight away.
I don't think there are any ships which would have symbols to give you extra cards.
However, you are correct that some captains do give extra cards (extra 1 card).
So, once more the card count:
* Choose 2 of the Stock cards
* Choose which of the decks you draw 1 card
* Possibly 1 from captain cards (if there are correct symbols)
* 1 for each improvement of correct type (attack card for attack improvements and so on)
* 2 destiny cards
This should give you 5 card minimum in every occasion, but
to get more than 8 you would have to invest on improvements, radically.