The main portion of the grade will be based on the tests and quizzes. Next the project will count for a significant portion of the grade. Classroom participation will count in the grade as well, but to a lesser degree. Finally, problem sets will have minimal or no weight in determining the grade. The last point needs clarification.
Homework is among the most valuable tools for learning mathematics.
It is vital that you work everything out for yourself. However, the specific amount of homework you do depends on the extent to which you are grasping the material. If a concept for you is simple, doing a few problems to check your understanding should suffice. Working on homework together I think working in small groups on homework problems is a terrific idea. However, it is a waste of time to simply transcribe the work of another student.