You are still responsible for restitution and court fines.  You would make payments directly the court or agency that ordered the restitution (in the sending state).

Reporting requirements vary by state. The state in which you will reside will communicate reporting and/or registration requirements to the probation or parole offer, who will in turn, communicate requirements to you and your legal guardian.

 Yes, if you are a on probation or parole, you are eligible for a transfer of supervision if you meet the following criteria:

You must ask your juvenile probation or parole officer if you need a travel permit, as they are required for some juveniles and optional for others.  If you are required to have a travel permit, the officer will submit the notification to the ICJ Office before you visit another state.

You must let your supervising officer know immediately if you must relocate with your legal guardian.  A travel permit will be issued for immediate travel or relocation, prior to a transfer of supervision case acceptance.

The receiving state is required to accept your transfer case if there is no legal guardian remaining in the sending state (where you were adjudicated), but there is a legal guardian in the receiving state. 

A transfer of supervision request must be submitted so that you can have a probation or parole officer in the state where you live. You must maintain contact with your supervising officer until the receiving state accepts supervision. The officer must still submit a transfer of supervision referral packet to the receiving state. 

The approval process may take up to 45 calendar days. To ensure the process occurs in a timely fashion, make sure that the person with whom you will reside is available for the home evaluation visit.

A person on probation or parole must be supervised by authorities in the state where they live.  The rules for how this works from state-to-state were adopted by law as part of the Interstate Compact for Juveniles.

A travel permit is written permission from your supervising officer that authorizes you to travel from one state to another. This permission is issued and submitted on an official Commission form called the Form VII, Out-of-State Travel Permit and Agreement to Return. Travel permits are required for juveniles on probation or parole who need to travel out-of-state for more than 24 hours if they were: 

If you are on probation or parole and need to reside in another state (called the receiving state), you must request an interstate compact transfer through your probation or parole officer. If the receiving state agrees to the transfer of supervision request, the you may relocate.