1) This sounds like you have some backlash.
Typically, you will see this when changing direction, eg, X moving right 10mm, and moving left 10mm, and not ending up exactly where it started, but moving left another 10mm (past the starting point), then back to the right 10mm, and will (probably) be where it started.
Backlash is commonly caused by some slack in either the leadscrew bearings or nut, and less commonly caused by slack in the gibs.
Mach3 has backlash compensation, where you can can tell it how much backlash your machine has, and it will adjust. Note that this will never be as good as removing backlash from the machine.
If you are moving in one direction (eg +x) as follows g0 x1 and actually move 0.98mm, followed by g0 x2 and are actually at 1.96mm, then you probably have an incorrect number of steps per unit.
If you find it is more "random", you may be experiencing missed steps. Listen to your motors while they move. You should not hear any "jumping".
2) I leave my machine on for long stretches. A lot of drivers have idle power settings for the motors, where they will reduce power by 50% for example.
3) Don't know. Sorry
4) This is a huge subject, and requires someone smarter than me to answer