That territory is considered full-friendly after you captured it during your turn.
So now that its after your turn, its defiantly friendly to the point where you can land planes there.
tl:dr Yes
I think you meant to say “definitely”
Okay so say a Carrier get’s damaged in battle, does it effect the amount of planes that can land on it?
Yes, before 2 planes can land; after, 0 can land
Yes, before 2 planes can land; after, 0 can land
Can planes on already stay on the carrier?
Yes, before 2 planes can land; after, 0 can land
Can planes on already stay on the carrier?
They have to stay. They can’t take off from a damaged carrier.