No you will not be able to deduct the down payment for a vehicle.

As for claiming business use of a vehicle, you can choose to take either the standard mileage rate set by the IRS (.54/mile for 2016) or you can take the actual expenses (gas, repairs etc) including depreciation. The depreciation is based on the total value of the vehicle but you are only allowed to claim a business depreciation expense on the business use percentage of the vehicle.

For more information, please click  IRS - Business Use of Car