Legal Question in Employment Law in California

I assume you are an at-will employee.

Yes, your employer has the right to terminate you. Indeed, so long as your employer has a reason that does not constitute unlawful discrimination, you can be terminated.

If your employer does not approve of how the shifts are covered, and you leave, or if you were not authorized to find people to cover your shifts, then you can be terminated or otherwise disciplined, at your employer's discretion.

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 terminated any time for any reason, with or without �cause�, explanation or notice. Unless you qualify for FMLA leave [which you have not described], you can be terminated. Keep the employer happy.