Im divorced and I want to marry my fiance who lives in the Philippines could I marry her just using my divorce papers

In the USA you do not need to present papers to marry someone.

Can I take my son and move to Russia if my husband decides to divorce?

If there is a Court order permitting you to do so, or if your husband permits it, then you will be permitted to move back to Russia. I suggest you...

Do I have any chances to win the case?

There is no "winning and losing" in divorce. It doesn't work that way. If you file for divorce and have been married for 6 months and jurisdiction...

Is my son responsible for his estranged wife rent, etc?

You son needs to follow Court Orders. At the same time he needs to hire an attorney asap to review the orders and find out what needs to get done....

How is the default date identified when counting the 20 years limitations on child support collection?

Very possibly. You may need to obtain counsel in NY to see what can be done. As counsel said, there may have been actions needed to be taken years...

HHow can I get a New Jersey court to appoint a new guardian for my Metally Challenged sister ?

You may wish to speak to a law school clinic or legal aid to see if someone will help you.

You should speak with an attorney who may be able to help you. Remember the father is in another country so it may complicate things.

If I lost my job and am actively seeking, ask for full custody because I am home now, I have a standard visitation rights

You need to immediately file a downward modification for your child support obligations or they will continue as ordered.

This is an unusual, but can I ask the previous jdge to testify? She still refuses visits + can "do no wrong" in this jdg's eyes

Almost certainly not. I wouldn't even waste your time asking.

How can I get my son passport?

You may be able to get a court order. I suggest you consult with an attorney.