What you are hoping to accomplish is really complicated, and frankly speaking, it can't be done.
First of all, Quizzes in Canvas are always done individually. They cannot be set up as Group Quizzes. You can set up Group Discussions and Group Assignments, but not Group Quizzes.
Secondly, I was confused by what you meant by "forums." Canvas doesn't have "forums." Are you referring to the Group Discussions?
In Canvas, you can set up overall Module Requirements, including prerequisites, for the entire course. However, I'm not sure if that will carry over to the Discussions that students can access through their Groups.
Lastly, I think this scheme is entirely too complicated for your asynchronous students to figure out. It will create too many questions for them and too many chances for students to get lost in this maze of instructions. If I were a student in your class, I would be really frustrated if my ability to participate in a Group activity and receive a grade for it was contingent on other students figuring out how to take a pre-quiz.
Honestly speaking, I think you are overthinking this project. If you were teaching in a face-to-face class, you might just be able to pull this off. However, this scheme is just too complicated, and it's going to create headaches for you and your students.