Generally speaking, planes don't just spawn. There are a few occasions however in the campaign where airgroups are spawned to represent historical air attacks.
But usually if you run into an aircraft it means there's either a carrier or a land airbase around. And yes, carriers move much faster than your sub, most can exceed 30 kts.
Also, if you are spotted (by either an aircraft, ship or land unit) they know you're there and they'll keep sending planes after you for the next day or so. Radio reports you send often have the same effect as the enemy picks them up and triangulates your position.
One Drambuie for me please!
