Axis & Allies Developer and Playtester; War of the Ring Editor and Playtester
An air unit has to stop moving when entering a hostile space.
No, it doesn't. Air units can move through hostile spaces, in both combat and noncombat movement. See pages 13 and 26 of the Rulebook.
Now what would happen if the attacking player loses the naval battle and the embarked land forces never make the landing? Do the attacking air units need to attack on their own?
Yes, but they may retreat after one round of combat.
Then say the air units actually win the land battle, how would they return to land?
In the normal way. However, if there is no legal landing space within range, they will be lost.
If the target territory was an island, and their are hostile naval surface ships in the surrounding water, the air units from the land attack would have to make a combat move as part of their return to base which isn't allowed.
This is not an issue - see above.