While I think it had a brief career as a vaudeville house, the Mayfair/DeMille/Embassy was not ever a legit theatre. It really doesn't count as a lost Broadway theatre.
Regarding those other theatres, the Hudson is used for banquets, weddings and other events as a part of the Millenium Broadway hotel. The Edison Theatre is now the Edison Ballroom and is also used for events and parties.
Not sure what is happening with the Century, if anything. The Times Square was held up for five years by that ill-fated Marc Ecko store, but now, I guess, New 42 Street will be shopping for a new tenant. A few commercial and non-profit producers/
theatres had their eye on the Times Square over many years, but either the problems with street load-in are too insurmountable, or New 42nd Street just prefers the theatres to be repurposed, instead of being used for their original purpose.
Begin at the beginning and go on till you come to the end: then stop.