Illegal, most likely.

In what area of practice is the type lawyer I need to represent me?

Have you ever heard of a mechanic's lien?

How do I get him to abide to the agreement without it costing me a retainer's fee? I don't want it to get uglier.

It appears to me that both you and he have grounds for divorce. Get it started. Best of luck in the future.

Can default be entered when a case status says "case dismissed - binding arbitration"?

No, that must have been a clerk's error. Good luck in the arb.

When all was settled I noticed that my air bags was non functional throughout the whole incident can i suit the dealership

Airbags are not designed to deploy on a rollover. Probably no case.

What can I do ? They have spent a considerable amount of time in dog kennels in the past. They are five years old

You are the legal owner now. Tell them to go fight with the shelter's attorney.

What should I do!? I feel so much hated towards them as a business.

Report them to the USDA as well.

Do I have legal grounds to demand a refund?

That is a novel argument that would be laughed out of court.

Is any of this illegal? What repercussions could follow?

If the guy finds you, you might get a knuckle sandwich.

My question is does he have a case if theres no proof my dog was even around his cattle at time of there deaths.

Tell him to pound sand, and keep your dog close.