2. Cash is king. On the other hand, $16k in cash is a bit odd - among other things, banks are unlikely to let one withdraw so much without advance warning and approval. A simple solution is a cashier's check. You go to the buyer's bank together, ideally where you also have an account; you watch the buyer get a cashier's check / money order; you go to your bank and deposit it. Cashier's checks and money orders are essentially cash, and cash is king. (If the buyer wants to pay in benjamins, it's probably a good idea to watch them be withdrawn from the bank - you don't want any fakes slipped in...)
3. Basically, you negotiate the price assuming everything is as stated, but you demand that the car be first driven to a mechanic you trust to do an inspection. You pay for the inspection ($100, maybe $200, depending on where you live and what labor rates are). Ideally you do this right on the spot, though it might be an overnight affair; the mechanic tells you his opinion and what's wrong and what might be wrong. If the buyer refuses to have it inspected at the shop of your choice, you walk. But you also would probably not be the one taking the car and driving it to be inspected, so it's a bit of a hassle. (Many dealerships will be much happier to give you the keys to do it yourself, since they can afford the risk.) For a car like you quoted, this is reasonable. It wouldn't really be reasonable for a $500 piece of shit, that's more of a take-it-or-leave-it deal. And again, for purchasing, cash is king, and cash equivalents are acceptable. Personal checks are not.
7. Probably. Also ebay motors.