Many charter and low-cost flights reach Antalya between 11 pm and 4 am, especially in summer. With a pre-booked private transfer nothing about that is a problem. Before you fly, you give us your flight number. We follow the flight, so the driver knows your real landing time, not just the scheduled one. When you come out of baggage reclaim, the driver is waiting in the arrivals hall with a sign showing your name, helps with the luggage and walks you to the vehicle.
The price you agreed when booking is the price you pay. It is fixed per vehicle, not per person, and it does not change because it is night, because there is traffic or because you have extra suitcases. There is no night surcharge and no luggage fee. You pay in the vehicle at the end of the trip; there is no prepayment.