I have multiple businesses but only one vehicle. do I answer the questions for the vehicle for the second and third business the same as for the first?

Yes, you would enter the same vehicle for each business. Your total mileage & commuting miles (or beginning and ending odometer readings) would be the same. However, you need to report only the mileage specific to each business. The total business miles would be the sum of your entries for each business.

See red box on screenshot below.

Business Vehicles are reported under Expenses >> Vehicle for your business.

The easiest way to find this section in TurboTax is to search on "business expenses" and click the "jump to" link in the drop-down list, which will take you to list of business in your return. Start/Edit the related business then scroll down to the Vehicle section to enter or edit your vehicle information.

See also: Where do I enter my self-employment business expenses, like home office, vehicle mileage, and supplies?