I happen to be a member of the Paley Center (only $50 for a student, and I currently live in NYC), so I have some comments:
1) I'd advise to search by title, and, even more so, by words in the title. Searching by subject category or by personality names is problematic due to the quality of the cataloging (there are quite a few programs in the collection that haven't been fully cataloged), and some of the listings do not have full titles (for instance, the word "Magnificent" is missing from one of the listings for the Magnificent Marble Machine).
2) The viewing limit for non-members is two programs of no more than one hour in length, though, as pointed out, the strictness of this depends on how busy the museum is. Also, the time given in the viewing center is always somewhat longer than the length of the selected programs.
3) As for holdings, the game show collection includes, among other things, an episode of We Interrupt This Week with Gore Vidal on the panel, a Movie Game with some unlikely appearances, an episode available for viewing (and several which aren't) of a version of Information Please not in the common records, some local material, the two known color Bob Clayton Concentrations, the last episode of Johnny Carson's Who Do You Trust? run, and quite a few other rarities from 1949 onwards.