1. There is only one unique dimension relative to the mirrored surface: perpendicular to that surface. That is the dimension that is reversed: every point is symmetric with its mirror image with regard to the mirror surface. The problem is that we regard our mirror image as a different person with a different definition of left and right. For example, if you are facing north into a mirror running east and west, the mirror image of your hand that's on the west is still on the west and the same is true for the east. What has reversed is that your front, which is to the north, and your back, which is to the south, have images that are the reverse of this: the image of your front is to the south and that of your back is to the north. This imaginary person then defines a new right side that's to the west and a new left side that's to the east. Your own (real) right has an image that's also on your own (real) right, and the same with your own (real) left is imaged in your own (real) left.

If the mirror is on the ceiling, up and down is the direction that's reversed, in agreement with this being the dimension perpendicular to the plane of the mirror. Of course it's still the case that if you, as a "righty" perform some actions with your right hand, the imaginary person in the mirror will use his left hand; but that's his definition of left, not yours.

2. Beginning with the fact that north is at the top, recognize that if you are lying on your back looking up at the stars with your head to the north so that for the most part more northerly stars are upward in your field of view, your right hand is pointing west and your left hand is pointing east. If you were to take a photo of the stars, the ones on the left would be in the east (where the sun rises) and those to the right in the west, where the sun sets.

Then the question revolves on why north is at the top. Ultimately it has to do with the fact that most people, especially the ancients who started building star maps, live and lived in the northern hemisphere, where most of the interesting objects (sun, moon, planets) spent most of the time in the generally southern portion of the local sky.  When looking at that portion of the sky, north is definitely upward, and since you are looking south, west is on your right and east is on your left, and you need not even be lying on your back. I think the star-map orientation of north to the top probably preceded the application of north to the top of terrestrial maps, thus reversing the left/right orientation of star maps, as you are turning around to face the ground rather than the sky.

3. In order for nut rotation to replace and/or assist in tightening of the screw/nut combo, they need rotate, in an absolute sense, in opposite directions. So, as seen from the side where the screw head is located, the nut indeed must rotate CCW.  However, most of the time when we're considering which way to rotate the nut, we're on the side where the nut is located. When we do so we must turn our body around in order to see the nut. This changes the definitions of CW and CCW. So CCW as seen from the side with the head of the screw is CW as seen from the side of the nut.

Going through all the combinations of tightening and loosening and seeing it from the side of the screw head and of the nut, the best way to consider it is that with a standard ("right-handed") thread, turning either individual piece CW from your own point of view makes it recede from you relative to the other piece, turning it CCW makes it approach you. So if you're on the screw-head side of the combo, the fastest way to tighten the pair is to simultaneously turn the screw CW while turning the nut CCW if you are doing this by yourself (with the combo unit being supported by whatever hole you're attaching this to).  If however you have an assistant on the other side rotating the nut, the CCW that you see or imagine (if hidden from view), translates into CW for the other guy, as he indeed needs to make the nut recede from his point of view, while it's approaching you.  For loosening the combo, just reverse the above.