Great criminal law question. Best of luck.

Could my ex husband gain custody with his criminal background, history of domestic violence and mental illness?

I would raise all of your concerns in response to his Request for Orders.

If it doesn't work, try googling her name or hire a PI.

Can I as the custodial parent move out of California if the non-custodial parent is moving across the country to VA?

I concur with my colleagues. Submit a Stipulation & Order reflecting the new schedule.

Could I get some kid of custody rights to kids that aren't mine?

It sounds like you have the best intentions. However, the length of the relationship may be an issue.

Can a person being on State disability be a caregiver for a family member?

This is not a family law question. Best of luck.

(California) Is it possible I may ask the Courts to pay my support rearages, plus interest & order reimbursement from Ex?

I concur with my colleague. Do not do this alone.

Can I appeal my ex parte that was denied?

If it was denied,you can file on the regular court calendar.

my ex gf is due in July, how can I serve her papers in July if she may or may not have had it yet?

File now and serve now to ensure you have rights when child is born.

Do I have a case for termination of parental rights?

What would be the benefit? With his record, I wouldn't see a court giving him any substantial visitation time without rehabilitating himself.