Depending on the situation the subject could be understood so it is not always necessary. But here I suggest that since the simple present tense second person singular is the same as the subjunctive "aspetti", I think it would be better for DL to make sure we understand that this is the subjunctive by using a different person. "I hope he waits for me."
Yes, Want requires To when followed by a verb. The 'you' doesn't change that. I want you to wait, I want to wait.
The first sentence is different because the second part of it is a dependent clause: I hope...you wait. It would be easier to see that if a relative pronoun had been included: I hope that you wait.
If 'hope' is followed by a verb that is not part of a dependent clause, it will also require 'to': I hope to go home soon. Since hope doesn't take a direct object like want can, you can't get a construction like: I hope you to wait. You have to form a dependent clause instead.