Can I sign my rights over?

Only way for this to occur is if there is someone willing to adopt the child or the state brings neglect/abuse charges against you. Obviously the...

Yes you can request it. If it’s court ordered mediation the father would have to comply. If it’s not court ordered the father could refuse mediation.

Will the court give visitation to my child's father who has never even seen her now that he has to finally pay Child Support?

If he has had no contact with the child it would likely be a gradual access schedule with the initial part being supervised and not overnight.

First, you would need to have the privilege waived to allow a child's therapist to testify. If the privilege is not waived the therapist cannot...

What are the consequences of not disclosing a minor child on I-130?

I switched the practice area to immigration so you can obtain the best response possible.

As a step parent you have no requirements/responsibility to the child.

I have a judgement for child support arrears. Is there a statute of limitations on that judgement?

Yes you can. You may want to speak to the office of child support enforcement agency for assistance.

Is custody mediation, ADR, or regular mediation an option after being denied custody in court?

Meet with an attorney offline to review the order you just referenced, and to obtain much more needed information.

Can I get the money I put for the down payment of the house back in the divorce settlement?

If it was money earned prior to the marriage (and you can prove it) then yes. Otherwise, short answer is no.

My son is getting divorced and they have lawyers. His wife is thinking that my son is hiding some marital assets in my Trust

You don’t need to hire a lawyer if you don’t want to, but you would be smart at least to consult with one in person.