1. This is a matter of personal choice. I generally save different operations in different files for version control reasons, but there is no compelling mechanical difference between the two;
2. Only if you tell it to. Depending on your CAM package, it may issue a G28 or G30 to go home or to a pre-defined "tool change" point, or you can (depending on your CAM package) tell it to go to a specific position on a per-toolpath basis. On my XCarve (which uses GRBL, not Mach) I have a point defined at the centre front of the machine as the "tool change" point, and another one at the centre back as the "cleanup" point., where on the lathe, I tend to use a per-toolpath safe point. Note that it is on you to make sure you set up the toolpath constraints so you avoid fixtures if you use this functionality;
3. Assuming you haven't changed the workpiece zero point, all the CAM calculations are done to this zero. On mills/routers, it is common for the Z zero to change with toolchanges, but the X and Y zeroes will stay the same, so everything lines up; and
4. No - in fact, you shouldn't - but assuming the fixture touchoff points remain unchanged and/or the workpiece touchoff points are unchanged (e.g. you haven't machined those surfaces away during the last op) re-touching ot re-probing zero should get you back to the same zero point to within less than a thou.
Generally my mill/router sequence is this:
1. Home machine;
2. Touch off fixture or workpiece X and Y, zero X and Y;
3. Probe Z (which sets Z zero)
4. Load file for Op 1;
5. With Z all the way up, jog to the X and Y extents of the toolpath and ensure that I am in the boundaries of the workpiece (which is a check to make sure the zero was properly set in CAM - if I touched off the lower left corner of the stock, but CAM zero is set to the centre of the stock, this will show up here;
6. When I am happy the setup is correct, run op 1;
7. Manually change tool for Op 2;
8. If the tool for Op 2 has a different Z height, probe Z to set Z zero (my router doesn't have toolholders so I'm changing tools in the collet, which means for tools that don't have a height setting ring, tool length is undetermined and must be probed. For a mill/lathe with tool holders and a fixed tool length, this step is unneeded);
9. Load file for Op 2. Sanity check extents in the visualizer;
10. Run op 2;
11. Etc until done.