English hw! i'm helping my brother but I haven't had this material for a while!They should be simple questions

I'm American, I don't speak English. It's been many years since I studied this. It's been so long since I was in school. They didn't have History cl, it was Current Events. In the sentence, I believe the part "in both Europe and Asia" is a prepositionary phrase, I think that's what it's called. "Tomorrow our new neighbors will move IN. " "In" is the adverb. "THROUGH which door did Alice go?" "Through" is the preposition. "Joan will carry the project THROUGH." "Through is an adverb. I think those are correct.