Can I either A) get the puppy back or B) get some sort of shared custody?

This sounds like a tough agreement to enforce.

Is my mum liable to pay?

She might have to pay the bill but speak with a local attorney first.

How can I gain custody of my dog?

Unless she voluntarily surrenders the dog to you, you could contact the police and an attorney.

Who do I contact to make the farmer around the corner keep his sheep off my property?

Try your local animal control officer or police department.

While walking our dog her leash came un hooked and she attacked another dog what should I do?

Unless and until something happens probably nothing. You should check with a lawyer before you agree to anything so you can be protected.

It seems you will continue to have problems, which may only get worse, until you contain your dogs so take active steps to accomplish that goal.

What can i do if a local vet sold me a basset hound puppy sick?

Contact the state vet licensing board to see what help you can get.

How can I get my dog back if while I was out of town he went and microchipped and certified him under his own name not mine?

You should meet with an attorney in your area to see what proof you can put together and learn of your chances and cost of getting your dog back.

Contact a lawyer that handles dental malpractice cases.

Consult with a lawyer who handles these cases immediately.