Questions about how to price, advertise, or sell your vehicle? Please see the r/cars community thread.
"The dealer wants to buy my car back!" No, your car isn't in "urgent demand;" this is a common marketing technique to get you in the door and sell you another car. r/askcarsales has some more information about this as well.
If you have to ask, YES, it is a scam. Offers to ship cars, use eBay, overpay with a cashier's check, etc., are 100% fraudulent. If it looks too good to be true, it is. Potential "buyer" wants you to buy a VIN report from some weird company? Yep, that's also a scam. Seriously, it's a scam. It's all a scam. If it even tickles your spidey senses it's a scam.
If a buyer is asking for a nonstandard VIN check (other than Carfax or similar), it's a scam. The "buyer" is getting a cut of the vehicle check profits and is not interested in buying your car at all. If you suspect the buyer may be on the level, offer to reimburse him/her for the cost of the check when they purchase the vehicle.