The company deducts the expenses related to the truck because it belongs to it. However, your spouse’s personal use of a company vehicle is a taxable fringe benefit. The amount usually is reported as such on Form W-2. There is nothing for your spouse to deduct…the company deducts the business driving and there’s no deduction for personal commuting.
Loss from an unforeseen and sudden event that is deductible, subject to a 10% income floor and $100 reduction for personal losses.