You can also ask, "Why?" before you answer, yes or do. Example: Are you free tomorrow? Why? (What's up?) I'm inviting some people to my house for dinner. Oh, okay, I can make it. /No, I can't make it. I have a date tomorrow.

you answer Yes or No .it depends on yourself .when someone ask you this sentence .perhaps he wants to invite you to do something tomorrow

Not really. "Are you free tomorrow?" is a simple yes or no question. You can follow your answer with one of your questions Example: Are you free tomorrow? Yes. Why, what's up? The other responses you listed would depend on the context of the conversation. After you answer the question of whether or not you are free with a yes or no, you can say absolutely anything you like