Can my neighbor who just got charges pressed against her for harassment take pictures of my kids in my yard without permission ?

You should report this activity to the police.

How do I find out if my mother still has guardianship of my kids

Ask her or Check with the court or file a petition.

What happens when a father gets reported to CPS for leaving a kid in a car?

Make sure you hire an attorney and be on top of this.

Will my mom have to pay support?

No. But the support from the father would stop if the daughter moved out.

I do not think you could. You would need to make sure her insurance was cancelled.

How can I check if there's an order of protection again me.

You would need to be served or you can check with the clerk of there is a case with your name.

Can the non-custodial parent take the child to a psychologist ?

It is true. You need permissions of the custodial parent.

Can I pay for my boyfriend to get a lawyer if we have a temporary order of protection?

You can meet and pay the lawyer but do not contact your boyfriend cause that will cause him to violate the order.

Can I file for abandonment against my wife who has left me with my son?

File for divorce and full custody of your child. There is no abandonment filing that makes a difference.

Who has a legal right over a child when the mother is decease?

The surviving parent has the right. You may need to take this to court.