In my neck of the woods tractors aren't titled like a vehicle or trailer, so, in theory, I could sell mine at any time and as long as I continued to make the payments JD wouldn't know I no longer owned it since no title changes hands. If I ever defaulted on the note I have no idea what their recourse is - other than suing me. I would ask the current owner to connect you with the company who financed the tractor for him. They should tell you what needs to happen to make them happy as part of the sale. If he doesn't want to cooperate it may give you reason to pause on the transaction.
As far as insurance, as others have said your homeowners should cover it if it's for personal use on your own property. Depending on its value they may charge a few $$/year on your policy. If you're going to hire yourself out there's a whole other level of insurance - do a search n this site, you'll find lots of good discussion. In any case, if you're buying private party you may want to have a dealer look it over and give you a written appraisal of its value. Also, make a folder with photos & serial numbers of the tractor & all attachments and give a copy to your insurance company, it'll make life much easier if you should ever have to file a claim.
-Norm