Wilma, you ask good questions.
Since I'm the one who pushed the hardest to have a mediation option, and particularly have only one mediator, I wanted to try to supplement Jn's already excellent answer.
It is very rare that people have exactly the same perspective about things. With more then mediator, the disputants are likely to get confusing or even contradictory advice, making it more difficult to come to a resolution rather then easier.
It is rare that a situation will arise that would allow for mediation (as opposed to an actual hearing) in which all the wrong is on one side. It would be the job of the mediator (as I see it) to encourage both sides to see things from the other person's perspective, and to attempt to find common ground, and to encourage a compromise that both sides can live with (even if neither side is completely happy with it). It would be a rare situation indeed in which if I were acting as a mediator I would suggest that one side apologize without the other side doing something in return.
The mediator would never have the power to decide what should happen. At most, she or he can make suggestions. A best case scenario is where the mediator helps the parties themselves mutually decide what the best resolution is.
I hope that makes some degree of sense.