1)
The motor shown, probably has no or low quality bearings. But for drilling (axial forces) it could work. Just give it a try.
If you use drills in a collet, you have to check if the drill diameter is stamped (bad) or laser engraved (ok).
You have to measure the runout of the chuck on the inside of the collet!
For PCB drilling, 0.11 mm runout is unacceptable (for me). Be sure to check if the chuck and collets are absolutely clean. It looks like the Chuck is heated to get it mounted. There could be some burned oil residues in the chuck.
There are no stupid questions, just stupid answers.
2)
Changing drills should not lead to a change in position. However, if If the drills are not the same height and there is no tool library, the Z position could be wrong.
3)
7kg.cm ok for positioning if the speed requests are low. You probably use Nema 17 motors. For the Z-axis you need some force to keep the drill drilling in stead of rubbing. But if speed isn't an issue, it could do especially if the PCB sizes are small. You could gear down to get more force. Keep the Z-axis weight low or add a contra weight.
There is nothing wrong with starting small and after a period of trial and error, learning, amazing and fun, you could go for larger steppers.