Depends on your contract. But yes they can just take the car back.
Yes. If you have not taken delivery of the vehicle, you can still back out of the deal. Find out what car dealers don't want you to know at www.dealertricks.com
Depends on the laws in your state. Go to your state attorney general on the web and look for a 'consumer' or 'consumer protection' link.
No, you do not. It's a down payment, not a security deposit.
The dealer cannot take the car back legally. It is their mistake and they will have to absorb the costs or mistakes that they made in the paperwork.
If you are a minor you cannot travel without your parents authorization.
What do you need the downpayment for? If it's for a mortgage on a house, then most states/counties have downpayment assistance for people. Search for it on Google, or I guess you can look it up in the yellow pages. If you want to search for it put "downpayment assistance" (with the quotations) in the search box and then put the name of your city, and press search. Then go back and try it with your county name. They have a lot of programs out there.
The dealer should be legally bound by the contract which the two of you entered into , a mutual agreement , unless there is an "escape clause" that the dealer can exercise as an option in the contract ; you would best consult an attorney regarding this matter .
I believe you can get your down-payment back if you do not have the car. But, if the dealer is doing that to sell the car after you have made a downpayment (depending on what the contract/receipt states) then you mave have legal options against the dealer. Some lawyers have free consults. I would contact a lawyer for free consultation before getting my down-payment back because the dealer may have breached a prior agreement/contract, whether verbally or written. State laws may differ.
That would depend upon the lending terms in the purchase contract, and in some US states the consumer law relating to the matter
You can of course return it but the dealer can refuse to take it back and in 99.9% of the time would refuse. After all the car is now a used car and cannot be sold as a new car any longer. The cooling off period law does not apply to the purchase of a vehicle new or used.
refuse to go back to Rome in chains