I know manufacturer-owned dealerships are out of the equation due to state franchise laws, but what do these laws actually say? Is it possible for a manufacturer to own and operate its dealerships if it buys up all of its franchisees?

I didn't read it but this may answer your questions.
http://www.franchisinglaw.com/

I know manufacturer-owned dealerships are out of the equation due to state franchise laws, but what do these laws actually say?

Is it possible for a manufacturer to own and operate its dealerships if it buys up all of its franchisees?

It varies state to state. When Daewoo came to the US, Daewoo America owned dealerships in a number of states. In states where this was not legal, they were forced to sell franchises.

From what I could find, GM owns at least two:

Miracle Mile Chevrolet Buick - Los Angeles, CA
Chevrolet Oldsmobile Cadillac Chicopee - Chicopee, MA

Source

BMW owns two dealerships in the NY area, BMW of Manhattan and BMW of Westchester. Does great things for competition and keeps the local dealers on their toes...