I realized that in guitars the strings are much closer to the top frets than the bottom frets. For example the string is much closer to the 1st fret than the 12th fret. Is it because the 1st fret is close to the nut of the guitar?

This is a silly stupid question to ask. I was wondering how you people switch your batteries of your active pickups. When replacing batteries I turn the guitar upside down and lay it on its backside on a soft surface. Is that a safe position for the guitar.

As far as the strings go, the headstock usually brings them a little down if not just straight across, while the bridge elevates them a bit, so naturally the strings will be further from the frets the closer you get to the bridge and closer to the frets the closer you get to the nut. Just the way they're made I guess. Not sure why that question needed an answer, but whatever helps you sleep at night, Curious George.
As far as safe positions for the guitar, I'm not sure there's an unsafe way to hold it or prop it up. Unless it's something that puts a lot of weight on the neck or something, I can't see how resting the guitar upside down would hurt it. It might make all the blood rush to its headstock, though (goddamn, that was cheesy. i'm gonna go hack a limb off).

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This is normal unless the difference in height is excessive.

Haha, Mortpayne