is person responsible for paying for the car if i accept their offer

Offers are usually made in good faith by some one who intends to purchase the item being sold. If no money is exchanged, then the party can always change his mind, unless there is a binding contract similar to merchandise sold on Ebay where, if the seller accepts the offer made, is entering into a contract and subject to a black mark if he does not buy the merchandise. According to my lawyer friend, when selling something, always try to do the transaction in person and even then, unless the purchaser commits to buy the item with his signature on paper, you can do nothing if he goes back on his word.

Unless you have a cash deposit you have no leverage at all.

A car is for sale until money and title change hands.

Not a deal until either a contract is signed or money changes hands.