Rideshare (Uber) but not his car. Can mileage deduction be used?

Let's answer each of your questions:

1. Can he use the mileage deduction for X? For Y?
   1. It depends.  Since the car X is not in his name, if there was a legal lease drawn up, then he could use the standard mileage rate, if not, then only actual expenses must be used and it is based on the actual cost for business use (business miles divided by total miles= business use percentage).  He would have to keep a reasonable record of mileage and any expenses to operate the vehicle. Items like gas, oil, insurance, rent payments would be deductible up to the business use percentage.  No interest or personal property taxes can be used since the car is not owned by him.  The same would apply to Car Y.
2. Can he use the depreciation for X even though it’s in my name? It’s practically his for the life of the car. It just has my name on it.
   1. No, because he is not the actual owner of the vehicle. He can use only expenses to operate the vehicle and rent if there is a reasonable agreement drawn up for leasing it.  The IRS would require ownership for depreciation expense.
3. Standard Mileage Rates  - This can be used for leased vehicles but must be used for the life of the lease if you choose this the first year.  If not, then only actual expenses could be used in all future years.