Can I refuse to work Sunday and still qualify for unemployment insurance in California?

No. If you refuse to work a certain day that your employer wants you to work, you will probably be terminated and not eligible for unemployment.

What does it specifically mean to hire a lawyer to represent oneself in a civil case to the opposing party?

If you are living in an unregistered unit, you should not be paying any rent. Regarding your issue, you should cease all communication with...

Cell phone audio recording

Yes, you can get fired for this or any other reason or no reason at all, unless you have an express employment contract stating otherwise.

Yes

What kind of attorney do I need and is this something I should pursue?

A full consultation would be necessary to properly advise you. There is no way to tell you whether or not you have a claim based on what you asked.

Can you sue a Surgeon for making a surgical error if your health plan contract calls for Arbitration?

No, you have to go through arbitration.

Can MY lawyer distribute my settlement without my consent? Also can he settle my case without my consent?

No to both of your questions. Bring this up with your attorney and if he still doesn't work with you, you can report him to the Sate Bar

Can i sue Time Warner for False price in bill

Just contact customer service and inform them of what happened.

I have been working for a company that provides mental health services for 6 mths and recently got caught shoplifting, what now?

You can get fired for any reason, including this. If they do another background check, yes, they may show up.

Debt Collection: For FDCPA, how to prove phone call violations if I can't record calls? (Re-phrasing previous question)

Your testimony will prove the phone call violations.