You absolutely have not lost the ability to view your library items by subject. You're used to using the filesystem as a kind of fake metadata kludge; now you have real metadata. Specifically, you have the Tags field, which you can populate with any categories you want to use -- and as many as you need. A book on both botany and zoology, for instance, could be tagged "botany" and "zoology", and you wouldn't have to try to remember which one you stored it under; selecting either tag would pull it up. The tag list is your "20 or 30 large subject categories", all conveniently available from one screen.
The Series field is, as you suspect, what you would use for the volumes of the "Harry Potter" books, etc. It wouldn't be a very appropriate substitute for the Tags, because you can assign a book to only one Series. If you had, say, An Illustrated Flora of the Northern United States and Canada, which is 3 volumes in printed form, you'd use that as the Series, and the number field would properly number them 1, 2, and 3.
Maybe I am the most clueless calibre user on record, but I can't imagine why someone would reject using the Tags field for subjects, and try to make the Series field do its work anyway.
Read the link in my .sig for why you should let calibre do what it does, and leave its private library alone.