If your town has a leash law (and most do) and your dog was not on leash, then it will likely be viewed as both parties' fault. The fact that your dog's collar came off during the fight might be negligence but it is not "neglect". The fact that the other owner didn't know her dog was loose is irrelevant. I wouldn't worry about the other incident unless your dog was deemed "dangerous" and it does not sound as if she was.
I assume animal control or the police were notified and I don't know what the other owner is asking for, so it's hard to say what you would be liable for. In most instances liability would be the vet expenses relating to the fight and the replacement value of the dog.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
This could be governed by ordinances that are specific to your city. I would check with a local attorney.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.