• the question is vague but not stupid ask again with better guides. Like how far above the earth the plane was, where it took off from, etc.
• u mean a helicopter?
• What do you mean by "stopped"? If you mean stopped relative to the solar system, then that plane is really travelling at several hundred miles per hour relative to the Earth's surface and it would come down at the furthest point on a line of latitude. This would only really be the "other side of the world" if it started near the equator. If you mean stopped relative to the Earth, and the plane is really a really big helicopter so it can hover for 12 hours, then it would land below where it was hovering.
• clearly it would depend on how fast the plane was moving and exactly where it was flying around the world. If it were around the equator, it would be longer, but say it were flying around one of the poles, then it would definately take much much longer, you should be a little more specific in your question yo
• If a plane was able to hover above the Earth for 12 hours...well that'd be awesome. However, no...it would not land on the other side. The atmosphere moves with the planet. The wind might push the plane a couple of hundred feet during that time...but it would still be in the relative location. Gravity might also add some resistance, keeping it above the same area.