The buyer does, seller can sell without registration on it, it is up to the new buyer if he/she wants to register it.
I think it may mean that the seller of the vehicle will "hold the loan" or will let the buyer make payments to them and once paid in full, seller will then sign title over to buyer.
A car buyer is actually the ones who will buy a car from a car seller.
There is no issue in buying a car from Ebay, as with any seller, it is buyer beware. Once finding the car you are interested in, you should physically inspect it and see it in person.
The seller will get the title. It may vary in different states, but I would suggest the buyer have a notarized document prepared which has a promise that the seller will turn the vehicle/title over. It a chance that buyer will take.
The buyer doesn't get the car.
ABSOLUTELY NOT
If you are the "private" seller you do not collect sales tax. If your states requires sales tax to be paid on a private sell then the DMV will collect it when the buyer registers the car.
Depends on the policy (rules) adopted by the seller. It's not a law in most places.
The buyer.
Most states require that the seller notify the DMV within a specified period of time that the car has been sold. If you do that, you should be relieved of all responsibility for whatever happens after the car is sold, whether or not the buyer registers it. If you haven't done that, you should do so without further delay.
Not necessarily but some states require you do so. My son moved to NC with a free car and had to pay sales tax.
Probably not. That's pretty much up to the seller. But in court it will probably be counted as rent paid towards the car during the time the buyer used it and the buyer won't get the money back. If the buyer were paying on the car, but never had it in their possesion, it might be different. But I'd still say that it's up to the seller.