Richard is distinguishing between what is proper and what comes from the American English. I'm American. So I can tell you what sounds right to me.
1) I don't feel like anything in particular. I'm not interested in eating/drinking anything in particular.
2) I would not say like that. I would say, I'm not feeling like eating SOMETHING now. If you have established what "it" is, then I might say, I'm not feeling it anymore. Meaning, I was feeling like getting a pizza but not I'm not longer feeling like it.
3) Here I would again say, I don't feel like going out tonight rather than I'm not feeling ....