can a used car dealership let you drive a car off the lot without a safety check?

If you paid for the car in full, then the dealership didn't do anything wrong. If you have a loan, the lender will require you to have an active insurance policy prior to taking delivery.

As far as docs, you should have a copy of the buyers order/bill of sale which proves you are the new owner. Safety checks are not required, however depending on which state you live in, there may be emission requirements. Good luck and I hope this helps.

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The dealer is supposed to carry insurance for the test drive. Safety checks are not required. If you get in an accident on the test drive, the dealer will file an insurance claim, but they will come after you too. Their clean insurance record is important to them, it keeps their rates low. If you bought the car, you are required to get insurance immediately. They usually require you to show proof, but the law is different in some states. You usually have 30 days to register it, and must have insurance before you can register it.

Well, that's just as much your fault. I don't think there's any law requiring them to check the vehicle for safety issues, though depending on your state it may need to pass inspection before you get the actual registration.

I don't think there's a law requiring a safety check. Most use cars are sold as-is, so you have to be absolutely sure it's up to your expectations before signing ANYTHING. You probably should have taken it to a mechanic before buying it.

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Once the car belongs to you it's all on you, not the dealer.

He's got his money, the car belongs to you, why should he care.

These are all things that the buyer is responsible for.

When it says no warranty it's up to the buyer to have it checked out before purchasing it.

Yeah, they did very thing correctly. You messed up for not getting it checked out prior to buying. You provide insurance not them.

They are in the business to sell cars. They don't care what happens after you leave the lot.