Generally speaking, does a Network have 100% total control of what day and time a wrestling show airs on their station, or does the wrestling company have any input? I would think it would be the former, as I can't imagine any wrestling company that would willingly put their program on a Friday/Saturday night time-slot when there target demo isn't at home.
Depends on the network and the wrestling promotion and the show. Smackdown is on Friday because FOX wants cheap programming to fill the "sports" niche on Friday nights precisely because no one was watching that night and they wanted an audience there. Ultimately the shows produced by the wrestling company are content to be programmed by the network, same as any other, so they can offer input and suggestions, but really it's the call of the people broadcasting the show.