A. A Justice of the Peace is a court. They can issue fines and, in some cases, jail.
B. To get into a state district court, the amount at issue must exceed some reasonable value. In my state it is $2000. (The amount must exceed $10,000 to bring a suit in a federal court.) Things may differ where you are; you can always call the clerk of your local justice court and ask.
C. I've collected $750 in the Justice Court for unsolicited faxes (three times at $250), plus reimbursement for filing fees.
But I haven't gotten an unsolicited fax in like forever. I think the scum-suckers have a background information network.