US statute of Higher Education System
One of the key things about U.S. system of higher education is that it is, for the most part, not regulated by statute.  For all of the "rules" that you explained, there are institutions that do not follow them (except the freedom to depart, which is guaranteed not by regulation, but by the lack of regulation, which creates a free market).

In theory, anybody in the US can found an institute of higher education, at any time, for any reason.  People in fact do create all sorts of new institutions all the time: some turn out very well, and some do not.  In practice, admission to the "club" of credible institutions is regulated by accreditation organizations, such as this one.  Every institution that can meet the fairly basic requirements for accreditation can set its rules as it wishes.  Public universities are typically regulated by the state that runs them (e.g., U.C. Berkeley) or the relevant federal agency (e.g., the Naval Postgraduate School), but private institutions like Harvard have a great degree of freedom in how they organize themselves.

In short: there is no document for the rules on how the system works, because the nature of the system is that there is no system, only a market loosely managed by accreditation.