Loan payments are not deductible.  The interest on the loan is (times the business percentage of use of vehicles).  Neither are the down payments.

You capitalize and depreciate the entire purchase price of the asset, not just the down payments (your question isn't clear as to the amount capitalized/depreciated).

Why are there no expenses of operating the trucks (at least gasoline...).

I think you need to provide more detail.  Something doesn't quite add up.