Once paperwork is signed and the customer drives off the dealers lot the deal is done.
The only time numbers can be changed is if the lender has not paid the dealer yet. If that's the case and the dealer is willing to lower the price good for you but it would be very rare because they have no legal obligation to.
What might happen is you will agree on a price lower then what you paid and the dealer will cut you a check for the difference. This will not change your deal as far as payments or interest rate goes but it will lower the amount of profit the dealer makes.
Good luck.
You can always use the new loan to pay off the higher interest loan the dealer sold you. If they won't budge on the price, tell them that's what you'll do. If the loan is paid off right away, the dealer loses their fee on the original loan.
It's not likely. Once you negotiate the price, that's it. You don't get to renegotiate after the fact.
Until you and the dealer signs the agreed purchase / sales price, the dealer can change the price at any time. Once the price is agreed and signed, it cannot be changed.
NEXT time do the research FIRST like any THINKING person does.