I don't know enough about Free Westinghouse machines to know which belt. The serial number for your Singer matches up with a Singer model 99K from 1956. Sew-Classic.com will have belts to fit it. Just let them know which machine you have and they will be able to tell you if you don't see your model listed on the site.
I have no recommendations about the book. Sounds like something I might like to read though.
Sorry, not much help.
Rodney