Legal Question in Employment Law in California

Unless you have a union or personal contract, or civil service rule, to the contrary, yes.

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.