You can assign planes to patrol. They will intercept enemy planes that attempts to attack carrier and the rest of ships in stack.
No. Same with, say, Galleys, you can't have them show a Settler unit standing around on deck if you place one into it.
Is another unit possible?
No...you cannot add units to other units in the game. You could change the image by modding.
As 2pop mentioned, try the "patrol" option of a plane(s) stationed in a carrier. the planes will hover over the ship. Not exactly what you mean but it is cool
Is it possible with modding?
I'm sure but you are talking about art...changing the image of the ship
Try the patrol feature
Otherwise, I do not know what to tell you. Check the modding forum
If you want to change the way the game shows the plane, on the deck, and then have it disappear if shot down, you need to mod the program artwork and the way it is invoked by the actions code. To find out about that, you should post your question in the "Civ4 - Creation & Customization" forum, not here in the General Discussion forum. The other forum is where the people who make changes like that discuss things.
Sorry go to"Civ4 Creation & Customization" forum
Last says
When a plane departs, it must be removed from the deck. And When landing have to see it.
Is it possible?
It is not possible to do what you want to do without modifying the game code. This is called a "mod". No one in this General Discussion forum can tell you how to modify the game. You need to ask in the Creation and Customization forum because what you want to do will require customizing (modifying or "modding") the game to accomplish it.