Basic Question

I would say that this question doesn't concern planes most of the time.

While k>0 in machine coordinates (and without any feature above),a single position is enough (often A0B0, if the stem is long enough).

For a cylinder, you have to turn around it, so I believe that turning the head at the right angle is better than using different tips.

You just have to check that the difference of radius between the ball and the stem is larger enough to compensate the difference of angle between the cylinder and the probe.

In addition, you can use spiral scan, which is always nice to watch :).

as long as the spherical probe is physically contacting the part "normal" to the surface (IE perpendicular surface vectors) it doesn't matter how you measure it.  it should be accurate.

If you are programming a one-off component, and will be using the routine only a handful of times i'd recommend rotating the probe to match the surface or axis vector as best as possible. Just know every probe angle change adds some uncertainty to the method of measure, especially if your probe calibration strategy is lax or uncontrolled to a master probe.

contrasting point of view: if you are producing a routine for high volume that will be used 24/7, getting MSA'd, and locked down with config management, i'd program the routine using star probes and minimizing probe angle changes as much as possible. The less probes and probe rotations used: the more your wrist will last, and the less probe angle uncertainty you will experience when operators crash this probe and not the other probe.

When i started at this place 8 years ago, we would burn through a probe wrist (PH10MQ) every 1.5-2 years, running 24/7.
since i've updated a majority of routines aligned with the second strategy, we've got 4 year old wrists still going strong.