Is an agreement to sell a car after inspection binding, and if a higher offer is made before the inspection, is it permissible to sell it to another person without sin, and does the hadith: "The two parties to a transaction have the choice as long as they have not parted ways" apply to it?

If the price has been agreed upon and both parties are content, then you are not permitted to sell the car to anyone other than the first buyer, unless he relinquishes the purchase or agrees to its sale to another person. It is forbidden to sell over a sale after the price has been settled and both parties are content, unless the seller gives permission. If there was a sales contract between you with an option to buy after inspection, then the commodity may not be disposed of except by rescinding the sale with the buyer's consent. And the "option of the session" (Khiyar al-Majlis) means that the two parties to the transaction have the option as long as they have not separated, or if they have stipulated an option for a specified period.