Spindle runout is checked with a tenths DTI mounted on the chuck or the wheel head. You want to test radial runout and also test the vertical back face of a GOOD wheel adapter for wobble after the runout is within a few tenths.
Flatness of the chuck is also tested with a tenths DTI, attached to the wheel head. What you measure is not necessarily what is going on, the table travel may not be in a straight line.
The last three are more involved. For checking and correcting the grinder geometry, reference "Machine Tool Reconditioning", it is far too long winded to type here...
The grub screws likely tilt the spindle in four directions, depending on design they could be pushing or pulling. My surface grinder does not have that feature, would need to be corrected by scraping on mine.