I think the stem in my tub faucet is installed wrong. When I first turn on the water it is hot instead of cold. I do not see a brand name on this faucet, but when I removed the c-clip I could not remove the stem. Is there a trick to removing the stem?

You may have a Moen faucet. Replacing these stems usually requires a special cartridge removal tool. However an advantage of the Moen is that when the hot is on the right you ony have to remount the handle 180 degrees and you get cold on the right. You don't even need to shut off the water.
If you have a faucet that is activated by the handle turning counter-clockwise then you may not have a Moen which usually has it's name on the escutcheon.
If this is one of the newer temperature balancing valves then the temperature limitation may be set incorrectly.

sounds like your valve is leaking the hot to the cold. (if the water then gets cold in a few seconds.) a small o ring is probably worn.or maybe the cartridge is.

The faucet does work in a ccw direction, and it is not a temperature balancing type. The water gets hot and stays that way in the cold position. Could it be that the cartridge is just stuck in place? If that is the case, how would I free up the cartridge?

Reposition your handle. The center stem in the cartridge only has to be rotated 180 degrees. Repositioning your handle does this.