Answers as follows: 1. There is very little 'meaningful' difference between the two sentences. Intonation might change the meaning, but in written form it is very difficult to distinguish any difference 2. It would be somewhat unusual to use either sentence. If you were trying to fix a broken heater and wanted to check if it was producing heat. If you were talking about a person it would be more likely that someone would say "Do you feel hot/warm?" or "Are you feeling hot/warm?" - either is fairly common 3. 'feel' is the stative verb