Are skin tumors painful for cats?

They're probably a little uncomfortable. Most of us have had warts and things along that line, and they don't tend to be terribly painful. If they're red and inflamed and oozing, they're uncomfortable, but by large, most cats aren't going to complain about a lump or a bump. They don't really complain about anything except something that just ticks them off. As you said, company, change in habits, or their food ball has a hole in the center, but they don't usually complain about not feeling well, or it takes a while to figure that out with cats.

Skin tumors can become painful for cats. When they are small, they may not be very uncomfortable. However, skin tumors can grow aggressively, ulcerate, and grow into tissue spaces, which can become uncomfortable for the cat.