Users are also granted specific permissions on SQL Server ...
First the sysadmin creates the user account and assigns groups. Then the DBA (actually a programmer who happens to be an MCDBA) assigns permissions to the tables. Or at least some of the tables ... the ones he knows about.
Usually there are tables (eg ones with user information) where users need to be granted/denied access per row. So you'll likely need to build the usual kind of permission scheme ANYWAYS. Having multiple permission scheme's is a good way to lead to confusion, and confusion is a Bad Thing when it comes to security.
Yes. Yes. And yes.

I also suspect -- but don't know enough about admin-ing Windows to be sure -- that this is actually a Very Bad Idea for SQL Server. I would think you'd want as few users with permissions on the DB as possible. And the one user with permission should be a user that no real user can be.