Flying Problem

Before flying, helicopter was on earth and hence its velocity with respect to earth was zero. when it flew above hanging steadily, again its velocity with respect to earth remains zero i.e. it rotates alongwith earth and hence its not possible to fly to another destination like this.

Imagine a car Tyre during rains. As the Car wheel rotates, there is most of the water from the road which is carried or rotated along the wheel. Now apply the same on earth. As the earth rotates - All air in the atmosphere is rotating along with the earth. Thus any object floating in such air also rotates along with earth. If not you will experience a heavy wind and you will be blown off. The reason why air rotates along with earth is due to the gravitational pull. air also has weight and thus experiences gravitational pull towards earth. This is why as the altitude increases - the air pressure drops.

However - the case is different if you cross the layer beyond the earth's gravitational pull. Example a rocket or a satellite. once it crosses - it cannot or does not experience and thus does not rotate along with earth.

It is due to a weakest force called gravitational force which holds the copter at its location and also it moves with respect to sun not with respect to earth

If with respect to earth we are steady , it implies that my helicopter too is rotating along with the earth as geostationary satellite(but this one near the surface of the earth) . thus forward velocity zero

Although the velocity of the helicopter with respect to the earth is zero, the distance covered by the helicopter is actually further than the distance covered by the rotation of earth, because it is flying above the surface of the earth. Consider a the earth as a circle with radius $r$ then the helicopter must be flying alongwith the circumference of a bigger circle with radius $R$ , where $R=r+h$ , h is the altitude of the helicopter). We know that $t=d/a$ , so the time taken by the helicopter to 'orbit' the earth will be longer. Since the helicopter is travelling slower than the rotation of the earth, isn't it that the destination will come itself?

the reason is newton's 1st law. the helicopter had an horizontal velocity along with earth when it was on the ground and hence will continue to have the same even when it is in the air

When the helicopter takes off from Earth, it has a perpendicular velocity that is the same as the Earth. This velocity remains unchanged and the balance of gravity and the helicopters engine maintain the helicopters distance from the Earths centre of mass. In effect, one can think of this as the helicopter being in orbit around the Earth, with its initial velocity coming from being chucked off the Earth and unless a force is applied to change that perpendicular velocity, it will remain in that orbit.

helicopter can't reach that destination because the helicopter exist in the earth's frame so, on this machine earth's laws will applicable;)

I think that, as long as gravity has a hold on the chopper... it will rotate with earth. The rotary forces of the chopper help it to "beat" gravity, but not completely, because it still has to have the rotor working to hover and balance it self with gravity. Thus the illusion of being "off the earth" but in fact gravity still has it grasp on it, so it will rotate with earth. Like you and me sitting on our chairs right now... or walking... whatever...