Can respondent file a response in harassment case voluntarily without proof of service?

Yes; by filing the Response you made an official appearance in the case - thereby waiving any defect in service.

Can I personally serve my husband divorce papers myself?

If by "signing papers" you mean "Notice and Acknowledgement of Receipt" (which only provides agreement to service), I suggest you take someone with...

I would say that it depends on the basis for the appeal; if it challenges jurisdiction, then ultimately the Judgment for Status Dissolution could...

How can I obtain my ex’s SSN?

Once the QDRO is prepared, you will need your ex to sign it, so assuming you are correct, when you have to file the RFO to get him to sign, you can...

What exactly does a stay mean in California divorce when my spouse was ordered to pay me but he appealed and the order stayed?

It's the enforcement of the order that is "stayed" because the order may be set aside. Your lawyer is correct that the appeal halts the proceedings.

Do I need to transfer child support and child custody case if we both moved out of county in order to modify?

You don't need to transfer the case and if you wanted to you would have to file the request in San Mateo so you might as well file your RFO there.

Is a foster parent also considered the foster child's guardian? And what exactly does guardianship mean in this setting?

You need to report foster's refusal to the social worker for the case - assuming it's a DFS case.

Travel request must be submitted 30 days prior.Itinerary must be provided.BOTH 30 days prior or can itinerary be provided later?

You would have to clarify with the court by filing an RFO but I'm sure there's no time for that; perhaps you can create an potential itinerary...

How do I present a case to the judge for school

You just need to elaborate a bit on what you posted here - what are the benefits of the school(s) that you prefer.

Can I be stopped from seeing my child?

I suggest you discuss it with her before you file before the act of filing will likely to cause her to become defensive. You have to communicate...