Is it helpful or unnecessary to get a police report for ex's failure to comply with court ordered exchanges?

Contempt is very difficult to prove as a pro per. Don't do this alone.

I concur. Hire a lawyer. You need help and input in design with the county.

Correct. If no response is filed then case can be dismissed.

Is there any way that I can keep my daughter away from him legally? Will I get in trouble for violating the order?

File for a restraining order immediately either at the self help center or hire a lawyer.

How can i take a father name off the birth certificate?

I concur with my colleague. Step-parent adoption is the way to go.

Court ordered visitation time no longer works with my work schedule

File an RFO. He can always volunteer to pick up if your schedule does not permit.

How, Theft, Fraud, Family

Take a change of address form to your dad and use your address. As for the belongings, what proof does he has that they are his?

Was it legal to record my phone call with my dad?

Yeah. I would look into how you can remove this admission from Aavo.

Is there anything else I can file or any other way to fight this or speed it up?

You could have filed an Ex Parte for the return of the child with an order shortening time in the alternative.

Can my friend take the child to California without issues?

File your request for orders. Never move without doing so as it may come back to haunt you with a vengeance.