Yes.

This is correct but only in an informal setting. You would only say this to a family member or close friend :)

Yes. They mean the same thing. I don't think it is really informal in American English though. If my boss were talking to me about food at the coffee machine at work, I would still use it with him. :)

There's an old ad for a ready-made sauce called "Chicken Tonight" (just add chicken). https://www.youtube.com/watch?v=mJ9M7bsx10I So yes, "I feel like ____" is natural when it means you want to eat something. We still make the joke, "That's strange, you don't look like [pasta]!"