Hi,

1) there are 3 or 4 default carriers in FSX, but they DO NOT have any arrestor cables or catapult, so you'd better try with a Cessna only. If you are confortable with panel editing, then you may want to give a try to the arrestor cable gauge that enables a plane to land on a carrier as if they were arresto cables on it

One default carrier can be found not far away from San Francisco, some miles away from that big red bridge, I'm always confused with the name, so I prefer not to name it 

2) with FSX you can now fly in network with some friends of yours, that's the best solution. However, if you prefer to fly alone, you should try the "Recorder Module" available here at simviation. It will register you while flying, and then create an AI plane that flies exactely like you at that time. So basically, you get the chance of flying with yourself