DOES DRIVING FASTER USE MORE ELECTRIC POWER?

In short, driving fast does use more electric power, and the same is true of combustion cars, to an extent.
Air resistance when a car is travelling fast means more energy is required to keep the car going at speed. However, for combustion engines, this effect is mitigated by the efficiency of higher gears. In EVs, there is no gear consideration.
The most fuel-efficient speed for a combustion car is higher than for an electric car.
Impact will vary by manufacturer and will depend on aerodynamics and electric motor and battery specification.