"My treat" means "I will treat you (to dinner, a movie, etc.)" or "I will pay for it". "You're on" is similar to "I agree" or "Let's do it". It's also used in response to a challenge or a bet. I'll race you across the pool! You're on! Your question was worded correctly. It requires "do" because you were asking about two things.

I agree with Susan's explanation and want to add that in this case the father is accepting the child's offer in a very enthusiastic way. There is a hidden meaning that he will hold Hannah to her offer. (hold to... meaning he will be sure that she does pay.) Nothing was wrong with your question until we reach (2). It is hard to correct here as you don't want me to "change" your sentences in the correction. Also there are no correction tools here. So, 1. You need a comma " 'your on' ". 2. You have a string of "so's" in that sentence. Use some periods, semi-colons, commas or a combination of these. 3. its not "it" ---> should be: it's not "it" 4. its wrong --> it's wrong 5. means --> mean 6. dont --> don't 7. correction requires a period after it. 8. Use " or [ but not both for the same purpose. Be consistent. I think that was thorough enough! :D