Can she move the kids out of state after filing for divorce?

The reverse side of the Summons prevents her taking the children out of the state and by filing she is bound by it.

Yes - file a Request for Order for Visitation based on changed circumstances of sobriety and stability and willingness to test randomly.

Can grandparents seek custodial rights/visitation with death of a parent following divorce?

They can but they must show an existing strong bond with them and that it would be in the children’s best interest to continue their relationship.

I just found out the judge assigned to hearing on my child custody case is biased few days before the hearing & want to change?

...and by “paper her” you file a 170.6 form.

The Certification of Trust is a summary of the actual Trust so you answer lies within the document.

Does my boyfriend need to provide more money outside the court order to send the child to private school?

He is not obligated to pay for private school.

Within how many days should opposing counsel file for opposition in a hearing?

Any opposition should be filed and served 9 court days prior to the hearing.

He isn’t asking for custody (and needs to overcome the presumption per FC 3044 because of DV0) but the court will grant him visitation. Start...

How can I get custody of my 4 year old son?

You need to file a parentage action along with a Request for Order for custody. Here’s a link with info: https://www.courts.ca.gov/11298.htm

The father of our son claims there is paperwork I can fill out and have him sign to disassociate him from my son and myself. Is

No such thing.... although you can refrain from requesting child support.