Yes
Yes, there's a dedicated shuttle service that will take you to and from the airport gates & car rental site. Complimentary rides.
Yes, Broward County buses, dedicated to the airport, will take you from any of the four (4) terminals to the Rental Car Center. Pretty much all brands available. Free bus from terminal to rental car terminal are easily identified and run about every 10-15 minutes... Enjoy..!
You can rent a car just there. I think is 5 floor
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