...starting after the engine is hot? The engine rotates but wont turn. When it cools down after 45 min-1 hr, then it starts with no problem. I've also had the check engine light on for quite a while with a P0420 OBD-II code (Catalyst System Efficiency Below Threshold (Bank 1) but I'm not sure that this is related to the problem of not starting when the engine is hot. I've also noticed that after driving on the highway, when i release the gas, the RPM fluctuates up and down for a short while then slowly drops off to normal. Is this related??

It sounds like you might have a Bad CAT. I have fixed the same problem before. A bad CAT causes all sorts of problems.

bad coil or oxygen sensor

you should probably have it checked out at a dealership

Hot engines are hard to start when they're too rich or flooded with fuel which would account for problems with your catalytic converter that has to burn the excess fuel in the exhaust. A cold engine start needs extra gas, but a hot engine start doesn't. The fuel vaporizes well when it's hot. So I would have a fuel pressure gauge test done to see if your fuel injectors were leaking fuel into the cylinders. Also check the Engine Coolant Temperature (ECT) sensor and make sure your air filter is flowing the required volume of air to the engine.

did you have the coil checked?, it could be getting hot and breaking down.