What is the typical Legal Structure of a modern College?
As I understand it, in a typical private U.S. research university the different colleges or schools that make up the university have no legal independence, and they are simply administrative units within the university.  (On the other hand, part of the endowment generally consists of restricted gifts, which can only be used in certain ways or by certain departments.  This can give the corresponding parts of the university more power or independence in practice than one might otherwise suppose.)


  Do the Colleges have members, and if so who are the members? Are all the matriculated members, or just current students? Are the faculty members of the College?


This is entirely a matter of university policy.  Current students, staff, and faculty would usually be considered members of their corresponding colleges, but this can vary (and some universities just aren't organized this way in the first place).  In practice, this generally doesn't mean very much: it may determine some requirements for students in addition to departmental requirements, it could be listed as an affiliation on your publications (although departments are more common), it might give a few privileges such as building or library access, and it tells you how to fill out university forms, but it's otherwise not a big deal.