Can I go to small claims for replacement of household property and moving exdpenses?

This does not seem to be a family law question.

Your right to appeal a decisions cannot be taken from you so long as you follow the rules of appellate timing. It is unclear if this is in NY. If...

Does my state have jurisdiction over my child?

The state which granted custody keeps jurisdiction for the life of the order, unless it chooses to give up jurisdiction to another state.

How can I get my niece here in the US?

This is an immigration question........................................

What happens to one's property (owned before marriage or inherited) in case of a divorce?

Generally property acquired prior to the marriage is separate property. However what you should do is get a prenuptial agreement between the two of...

Can my husband have the kids overnight on a regular basis at his girlfriend house rather than his place?

He can unless there is an order saying otherwise. I assume you eject to this so take it up with your attorney. If your attorney and your husband's...

Can a non custodial parent, moving across the country, still keep visitation?

The question has nothing to do with the order. It has everything to do with distance. If the father cannot visit because he is hundreds of miles...

Child support on external account?

If he is paying you directly rather than through SCU and if he has records, he will get a credit for the amount that he is paying you.

No you cannot. If you disagree with decisions, you can appeal.

Not hiring an attorney in an action regarding your children is the worst thing you can do for yourself. You are almost asking for the Court to do...