I have not seen zero or very low rate car loans for used cars. You do see them for new cars, but they are just taking whatever they would have given you as a cash discount and converting it into a low rate. Maybe a bit more, as they charge fees on the loan that they roll into the balance owed.
I meant up-front loan fees like origination fees, etc. You're saying they don't have those? It's been a long time since I financed a car at a dealer. Also title work/documentation fees, warranties, and whatever else they might talk you into.
Not necessarily. When I bought a used car a few years ago I got a great rate (< 2.5%) from my local credit union, and the rate the dealership offered was almost as low. Rates are much higher across the board these days, but the principle should still hold.