Power output

No, not really.

For the car to be travelling at a constant speed, Newton's second law says that the net force on it must be 0. We know that there are two forces acting on the car: the friction force and the force from the engine. For the net force to be 0, these two must balance each other out. That tells you what the applied force from the engine must be. You can then use that applied force in the equation you posted above in order to determine the engine's power.

 

No, it's not 4000 N. Write the force balance equation for the horizontal direction:

sum of forces in horizontal direction = 0

and use this equation to solve for the applied force from the engine.

The initial condition is irrelevant here. You're told that, right now the car is moving at a constant rate of 10 m/s. This, along with the applied force, is enough info to determine the power output right now.