In order to ask for IFP status, you must file a "PETITION AND AFFIDAVIT TO PROCEED IN FORMA PAUPERIS" with the Court, in which you give the Judge detailed information about your financial situation. The required form is attached to these instructions, along with a form order for the Judge.
If you have been making your payments regularly and on time, restitution and other court-ordered debt shouldn't show up on your credit report. However, once you begin missing payments, the court can sell your debt to a collection agency that will likely report the debt to the credit bureau.