Answers to your list of questions:
No, I generally only need to look at next actions.
No, I generally do not need to single out particular projects as weekly prioritit’s.
No, the context lists have everything I think I might want to do, part of a project or not.
No, neither, my weekly schedule generally has rhythms built into it, but that’s it.
As you might guess from my answers, none of those practices are required for GTD. Following David Allen’s advice, I try to plan and schedule as little as I have to. Some people like to do more, but I find I don’t really need to. It’s actually a bit of a shock, to find out how free you can be. Like walls disappearing into thin air. I think I get more done and am happier too.