1: Object edit->insert will add an Edit point/Isoparm. If you actually wanted to add a CV, you could also rebuild the Curve to a higher degree using rebuild curve or the numeric boxes on the right. Theres a large discussion about the fundamentals of NURBS geometry (IE the difference between a 3 degree, 2 span curve, and a 5 degree, even though both have the same number of CV’s)
3: Those are guidelines, mostly useless unless you’re doing a lot of 2D construction. Delete them by going to “Delete->Guidelines” on the top bar.
5&6: I need to check this when I’m in front of the software, but you should still be able to pick the edit points of your CoS even if it extends beyond the boundry. As a general rule of thumb, I find you want to try and avoid editing CoS’s directly - it is usually easier and cleaner to create a 2D curve, project it on to your surface, and then if you need to modify the COS edit the original curve (as long as the history still exists it will update). It also usually makes it easier to reference other geometry to that part by referencing the original curve rather than the COS. If you can’t see the edit points just make sure that “edit points” is checked on your control box on the side so they are definitely displaying.