That's the whole concept of mediation. Yes.
If you want to know more, go here:
http://en.wikipedia.org/wiki/Mediation
You pay only what you agree to pay in the contract. If the mediation fee was not addressed in the contract, each party will pay their own mediation fees, as agreed to by the mediator and the party prior to the mediation.
A signed contract is a key piece of evidence. It shows that both parties agreed to specific language. Without it, the evidence of the contract and its terms has to be inferred from the actions of the parties.
It is wise to address such matters before the contract is signed. This is dictated by the terms of the contract the parties agreed on. If you've already signed the contract then you will just have to read the contract to find out.
Can you change agreement to a mediation after you signed it? What is the grace period?
Yes, you may sue anyone who breaks the items stipulated in any written contract signed and agreed upon by both parties in the first place.
It can be held to be valid. If the parties are acting as if both parties have signed it, it will be enforced.
If the parties haven't executed a contract signed by both parties then you are not "under contract".
A contract is a legally binding agreement between the parties who have signed it, unless written into the contract otherwise, all parties are bound by the terms of the agreement/contract they signed.
If both parties are in agreement to the terms. Otherwise any written contract, signed by both parties, must be kept.
Assuming you are one of the parties on the contract, Yes.
Only if both parties agree to dissolve the contract or the contract was an illegal contract or it was signed under duress.
Generally not. A signed contract is generally binding and requires both parties agree to terminate the contract and create a new one.