Talking to one of the other Dad's(his son plays football as well as rugby) at my sons rugby training just the other night and he said that apparently they have a problem getting referee's for that very reason.
Our rugby matches are different, I officiate at all my sons home matches.
Don't know about referees but anyone is allowed to be a linesman, every Sunday at my sons matches there's always arguments about dodgy offside decisions made by linesman connected to each team
Football referees have to declare any connection to a particular team to the County FA when they register each year. However such a declaration doesn't necessarily prevent them from being appointed to officiate in any particular match. (It's entirely at the discretion of the Referees' Secretary for the relevant league or competition).
Yes. It happens a lot in local junior football. When I was a referee a few years ago there was a rule in the local leagues- I think it was an FA rule- that if the official referee didn't turn up or the league had no referee available, the the officials of the clubs involved in the game had to agree on a referee between them. Sometimes each manager took half the game, although that probably wasn't really allowed as I think it's supposed to be the same ref throughout for consistency