Nothing wrong with handing over the keys without taking cash or cashier's check. Just don't sign the ownership/title over until you have payment.

If they take off, then the car is stolen and you can settle it out with your insurance company. That might be a positive in some circumstances.

Here in Canada Kijiji and Autotrader are THE sites to use. Both are free for basic ads.

With regards to the rest, it all depends on what the com parables are selling for. There's no sense in putting anything into a car you're only going to get 1k for. But if it's something that can make the difference between $15 and 17k then it's worth considering. Look for a good return on the investment you'll put in. Like 3-4x IMO.