How and what theta criterion should i use and how should I use the Projection principle in these sentences? [closed]

Question

1. John hopes to win. So far, I've understood that since to win is an infinitive clause, we cannot give any theta role, but I'm confused with the projection principle of it. Can I say that there are two predicates and only one subject? Or put the big PRO infront of to win? Is John the only lexical requirement for the two predicates?
2. Whom does John love? I understood that John is the agent but what is the role of whom and does? Should I use whom as the patient since it is a relative pronoun by following the deep structure? And if i transform it to deep structure, will "does" be added to indicate that the sentence is in present form? If i add the "does", will "whom" be the experiencer that is experiencing John's love instead of being the the PATIENT?
3. Mary and John plan to visit the store. Is the store the goal and "to visit" the same as "to win" in sentence 1. And since we can assign one theta role to one argument,Will Mary and John be given only one role together? Can you please explain it to me and correct me if my assumptions are wrong.