Is there a way to set and manage different level of Membership so that certain paying users can see/buy certain items on site?
Sure: 1) In admin>customers>customer roles create a Customer Role "Special Member" 2) In admin>catalog>categories create a categoory "Exclusive Items" and in the Acces Control tab deny access to it to the rest of customer roles
I see ...can a product belong to different Categories at the same time ?
Yes as many as you want. But if you include any of your "Exclusive Items" in other categories not restricted for other customer roles then anyone could buy it