They certainly could, a magnet floating in outer space is still a magnet, Earth just happens to have a massive molten core of magnetic materials.



I can't imagine any scenario for this to occur that wouldn't be absurdly catastrophic. It is caused by the motion of molten iron the outer core spinning and the amount of that iron out-masses the oceans considerably. As long as it is molten and moving there will be a field. However our electronics generally work just fine on places without significant fields like the moon or mars, and not very many of them function in any way that should be effected.



That depends on the atmosphere, or atmoplane, exclusively. On earth one can see 1.2 miles times the square root of the feet in height, roughly, or 12 miles at a 100 feet and 120 miles at 10,000 feet. At these heights the atmosphere is thinner and you can see through more of it, but of course the reason is the curvature. Several hundred miles at least though, through air, but not millions, and you'd have limited effective resolution.



Absolutely, on an orbital ring, such as an Oneill Cylinder, Banks Orbital, or Niven Ringworld for instance the horizon does not exist, as the world curves up, and the weather would be very different. On the moon you can see a very long way and crisply, from the lack of air, alternatively the world slopes away quickly from the curvature, you would have no difficulty seeing an object disappear over the horizon. Weather patterns are seriously effected by everything from planet spin rate to the moon and of course the sun and the magnetic field of the world. To your specific suggestion, a non-rotating world, these are probably quite common, like our own moon. A tidally locked world, one that always has day on one side and night on the other, would have very different weather, possibly a breeze always blowing out from the same sun-side point. However it seems probably, as I think we've discussed on the board before, that a tidally locked world would blow all of it's moisture to its darkside to be frozen in massive glaciers and be a desert on the sun side, so probably no clouds.