Well, I know that with the verbs give/bring, I can use: give somebody something or give something to somebody.
But, when I'm talking and someone says: "How should I do this homework". I answer: "Do it and next week, give me / bring me."
Is it right or do I need to say: "give it to me"?
In my opinion, the use of "it" wouldn't be necessary here.
Hand it to me: give
Carry it with you: bring
Bring your homework tomorrow, and give it to me.