If the doctor had no consent, explicit or implied, it may be a lawsuit.

That seems quite unethical. You may want to report this to the hospital licensing board.

No. The law that applies is was where you or living.

Many cities or counties have legal aid or other organizations that provide pro bono (free) legal advice and services.

Consult with and hire another attorney before firing your current attorney.

It depends on more facts and what the “cease and desist” said. Consult with experienced malpractice attorneys in the state where this occurred.

Charging fees in this situation would be illegal and unethical.

Yes. If you do not get an agreement to turn in as full satisfaction they can sue on the contract.

Show them why it is in their best interest now. For example, immediate money, collection will not be easy, etc

Look into a motion to set aside the judgment for failure to lawfully serve the lawsuit.