Graham's corrections are a more natural way of making those two statements , although your phrasing is acceptable in casual conversation . Your last sentence , however, is incorrect. A better way to say it would be, "Be quiet while your teacher is not here, will you?" This is because "will you?" indicates a positive action, and it references the beginning of the sentence, which is a negative (do not make noise). If you take out the supporomiddle of the sentence, you are left with, "Do not make noise, will you?"; you can sew that the positive doesn't work to reinforce the negative . Does that make sense?

You are correct; you would use "the" when using U.S. as a noun. If you were to use it as an adjective, you would not use "the". (For example "U.S. aggression has been a source of tension in the Middle East.")

Adventure Time is a cute show, but it uses a lot of made-up phrases that don't actually exist even in English slang. If you are using television to help with learning English, this show would not be my first choice, although there's no harm in watching it for entertainment and general exposure to the language.

し for 4 and しち for 7 are less-preferred because of their similarity to the word for death. They are still used, but not as frequently.

You would use an adjective to describe a noun, and an adverb to describe a verb, an adjective, or another adverb. Your answer is correct. You answered correctly. Your performance was perfect. You performed perfectly. He remained perfectly silent. He speaks extremely quietly.

Yes, the sentence is correct. Regarding your second question, “over this” is the more natural word choice.