I heard that what can make a helicopter go higher is the presence of
"Air" to power its engine.
The helicopter's engine is powered by burning fuel together with oxygen from the air, then its propeller forces air (not necessarily the same air which is burnt with the fuel) downwards to lift the helicopter upwards.
Let's assume that the amount air would be exactly the same at
different altitudes, would the power needed by the helicopter to stay
stationary at 50 meters high be less than the power needed to be
stationary at 200 meters (or even higher), or would it be the same?
Yes, it should be basically the same if the air density is the same. Air density is not the same at high altitudes like one or two kilometres, but it's approximately the same from 50 metres to 200 metres above ground.
Something called "ground effect", an improvement in performance, occurs within one radius of the blades from the ground. However, helicopter blades don't come as large as fifty metres. Apparently (from searching the web), the largest helicopter in the world is the Mil V-12, which has blades of radius only seventeen metres.