How do I record a vehicle that was purchased for the company but paid in full? Currently, I have it recorded on the balance sheet as a fixed asset? Is this correct?

Yes it is a fixed asset, and the payment you made should post to that same account

yes you calculate and post annual depreciation to a fixed asset sub account for the car called accumulated depreciation-car

download IRS pub 946, depreciation it has the tables and % per year for depreciation.

journal entry to make the posting

debit depreciation expense
credit accumulated depreciation-car

I prefer to set up the FA account sturcture this way (all accounts are FA accounts

Car (do not post to this account, it is a summing account)
>> cost
>> accumulated depreciation