To try to complete the answers:
1 - You choose your part origin on the machine in relation to a place that you can feel.
Choose clamping or reference faces in raw tone.
Then, either you keep the original CAD part and you enter it in the NC
Either you move your CAD origin in the CAM in relation to your machine
It's mandatory to have the same origins.
2 - See answer in 1
3 - The CAM software will give you tool lengths to respect so as not to machine your part with the cone chuck.
You have to adjust your tools accordingly on the machine
The compensator is only used to compensate for milling cutter or machine defects.
If everything is measured correctly, there is no need for a tool corrector.
On a ball, if you work in the center of the tool, you can't compensate for the Ø
You have to play with the thicknesses on the CAM software
4 - There are small measuring arms that allow you to feel parts.
Otherwise, caliper, finer, gauge wedge, or a 3d probe on your machine.
5 - I advise you to represent your clamps or other elements of your machine.
You can also draw the cone of your tool to avoid all collisions.