Legal Question in Employment Law in California

They sure can. Unless you have a union contract, are civil service, or have a personal contract of employment (which if you aren't "O" level management is highly unlikely), you are an "at will" employee who can be fired for any reason or no reason at all, as long as it does not involve racial, gender or other prohibited discrimination.

Yes. In general, unless an employee is civil service, in a union, or has a written employment contract, they are an 'at will' employee that can be disciplined or fired any time for any reason, with or without �cause�, explanation or notice, other than for illegal discrimination, harassment or retaliation under the ADA disability, Civil Rights [age, race, sex, ethnic, religion, pregnancy, etc], Whistle-blower, or similar statutes. The employee's goal should be to keep the employer happy. You're not doing so.