am i liable to pay past due support if not earning?

There is restraining order that asks $1000 per month "unallocated" spousal/child support from me. I am not in US and not earning. I have not appealed against the order.
1. Am I liable to pay the past due support if I enter US after a few months? Or am I allowed to demand a hearing first? Or should I file an appeal right now by hiring attorney in US?
2. What is "unallocated" support?

If you have been ordered by a court to pay it and you have failed to pay it, that doesn't erase your liability.

Yes. You still owe it. It doesn't go away if you ignore it long enough.

If you have questions, consult with an attorney in the jurisdiction where the order was issued. Many offer free initial consultations.