It may well depend on what state of the United States in which the video was recorded. Some states don't permit recording private conversations...

Can I make a claim with the other parties Insurance, and if they should denie the claim would I have case if needed be..???

It's hard to see how their liability carrier would be obliged to pay your claim, since there seems to be little if any fault on their part. If you...

Can an attorney or doctor have that a contract that says he is not liable for negligence?

No, there public policy reasons that is prohibited, and there's an ethical bar on putting such language into professional retainer agreements.

Got in a minor accident and let me go

He can sue you, even though he let you go. One reason you would want the police to come to the scene is for a neutral party to make a record of the...