Combo ships are only available if you play their faction combo. They can be found like any other ship in ship system locations then. You might have gotten unlucky so far or played combinations that don't have their combo ship unlocked yet.
As for fire mission, the card never says it puts the card into your hand. It is created in your draw pile on deploy, that means when first putting the ship on the board. Fire mission then remains in your deck like any other card until the encounter ends or the missile carrier retreats.
