If it came from space, you have to had put it there (and give it a velocity with respect to earth) before; this energy counts, too. Let's make a break for today, me at least; maybe you will see it differently too if you sleep over it :)

If it came from outside, it will move on. If it started from earth, it will remain (nearly) above the same spot. Why? Well, why not, because it initially has the velocity of rotation already. The same reason why we can remain where we are. What is the difference between sitting in front of your computer and hovering? There is no force on you when you are sitting either.

i reposted it as an answer and hope to have understood your thoughts more or less correctly

Yes, that's why airplanes fly so high. But it has nothing to do with earth's movement. They just don't care, that earth is moving or rotating. I assume, you wanted to use an object that comes from outside the earth (it doesn't have to be a helicopter, take some asteroid, they are more common out there) and use its movement to travel with respect to earth. This might work (theoretically, not in practice). But you cannot reuse the object, it will travel on after you disembark. To get it back, you need to put in energy, which you wanted to avoid.

Nope, the reasons are not obvious at all ;) a ball that can roll without friction is so perfectly spherical, that it will touch the floor in exactly one point. So what is the torque in the first case? ;)

no, actually my comment was not just humorous :) the air is not moving with respect to the ground (it sometimes does, but the energy is consumed by friction pretty fast; and wind velocities are negligible compared to the earth rotation) - so there is no way to neglect air resistance if you want to move with respect to the earth. Just no way.