Dealer sold by private, what to do?

Have found a nice car, which the seller allegedly bought recently, but only driven a few days by a short registration plate and now wants to sell again. But I like the car. What exactly does the used car guarantee contain? What happens now, then, if something happens? For example, the engine is over in half a year? If I can prove afterwards that he does this professionally? Because now have Googled his phone number and two older e ads found. But if the contract is sold by private, can that still be successful? I know, actually not serious, and you should not support such a thing, but I just like the car too well.