In the deduction section, they are asking for the cost of the new vehicle I bought. Is that the actual court, or what I have paid for the year?

Vehicles are not tax-deductible on a personal return.  Sales tax on a vehicle is deductible, but I don't know why the program would be asking for the vehicle cost and not just the sales tax amount.  In that case, you would enter the price on which you paid sales tax.  (For example, if the car was $40,000 and you had a $15,000 trade-in, so your sales tax was based on $25,000, enter $25,000.)

Vehicles can be listed as assets in a business, and can be depreciated or expensed as a business expense.  In that case, you would enter the agreed-upon price, including sales tax and any other required fees, but not including any costs related to financing.  For purposes of business expenses, the price is what you agreed to pay, even if you did not pay it all at once. 

Or, if this is an EV subject to a tax credit?  Enter the price you agreed to pay even if you are paying over time.  The EV credit is not available for cars that cost more than $55,000.