Well, let's see how many of these I can knock off the board
Generally, game show producers have their own production companies outside of a network (per say Mark Goodson Productions). They come up with a concept and 'pitch' it to several networks until someone expresses an interest in putting up the money to produce a PILOT episode. Once that is shot and edited, there's several things that happen with that episode in order to see what type of reactions will come from it. If the feedback is positive, then the network will order a certain number of episodes to be shot with "real" contestants to be aired. If ratings are good for a few episodes, they have the option to order more to be made.
I made be corrected by the people in the know, but generally these days networks start with 6 shows, option up to 13 for a one-night-a-week show.. and multi-week shows range 40-65.. and daytime shows go about 200?
Rights to a show are generally written into the contracts set to expire after a period of time of inactivity. Thus per say Fremantle couldn't just take PRICE IS RIGHT from CBS one week and drop it on NBC the next if CBS cancelled it.
Concepts remain with the production company, and the network hires the production company to produce and deliver the shows to them by a set deadline.