How can I find out who falsely accused me my case was unfounded?

Identities of complainants are generally kept confidential.

Conditional GC Holder - Pending I-751 - Do I need re-entry permit?

This doesn't appear to be a "Public Finance" question, so I'll reclassify it as "Immigration."

Is there a way to fight this cell-phone ticket, or at least not have it on my record?

I don't see anything from your post that would suggest a defense, but I'll change the practice area to "Traffic" from "State & Local" so you can...

Do I have a case in this credit card fraud situation?

I would report it the police, I don't see why they would laugh at you.

You don't give much to comment on. Speak with an employment lawyer to review the facts in detail.

It can be classified as such if its in a state of disrepair incapable of being driven, which it sounds like it was.

Not sure what you mean by your name is on it. Are you the registered owner? Or do you mean you're on the title? If it isn't registered to...

They can always ask for ID. Get a lawyer.

Is someone with a significant brain injury REQUIRED to have a person that is power of attorney?

Going to change the practice area from State & Local to Power of Attorney.

You should call the court clerk and ask.