If the operator is outside the train and does whatever he does to make it hover with respect to him, then the helicopter will be moving backward relative to the train. But if the operator is inside the train and does the same thing, the helicopter will be stationary with respect to the train.
RC helicopters go wherever the operator sends them, at least I think that's how they work. Maybe they have inertial guidance systems in them and when you tell them to hover, they stay put relative to the surface of the earth, in which case I'm wrong. Tell me what you know that caused you to ask this question.
I think he is asking why the helicopter does not move relative to the train once it is hovering. The difference is the initial momentum the helicopter has before it starts hovering.
From there the momentum of the surrounding air keeps it in place. If you send it out the window it will start moving relative to the train.
"Objects in motion will remain in motion unless acted upon by an outside force. Objects at rest will remain at rest."
An observer outside the train sees the helicopter in motion. What net force does he observe to act upon it? If he observes no force, then the helicopter will remain in motion with respect to him.
An observer inside the train sees the helicopter at rest. What net force does he observe acting on the helicopter?
If the helicopter held up by the air inside the train.The helicopter at rest but the train is moving forward. there are no horizontal force acting below the helicopter. will the helicopter move backward when the train is moving forward? An observer inside the train seen the helicopter is moving backward?
Does your question involve the mechanism of how an RC helicopter hovers? Could you have asked the same question about a helium filled balloon that weighs just enough to hover?
a) Train moving constant speed. Operator in train launches helicopter. It hovers stationary with respect to the car. Operator can't distinguish this from case if train not moving at all. Main factors are simply that the helicopter starts with the same motion as the train (from ground point of view) and is then carried by the air (moving with the train).
b) Train at rest, operator launches helicopter. Train starts to move. Helicopter will hit train wall (most likely). Moving air (relative to ground) not likely to be able to get helicopter accelerating as quickly as the train, so it will hit wall.