Legal Question in Employment Law in California

Not unless you have a contract with the employer that requires you to give 2 weeks notice. If not, either party to the employment relationship can end it immediately. The employer does not have to pay for days not worked.

Mr. Kirschbaum is correct. Generally an employee can be fired at any time for any reason except reasons specifically prohibited by law, such as racial discrimination or retaliation for union organizing. Since an employer can fire you at any time, you certainly don't get to suddenly guarantee yourself two weeks of employment by giving notice.

No, you quit and they walked you off. You are entitled to be paid for hours you worked.