"Ground - throttle controls RPM, prop control directly affects MP (manifold pressure)"
When you are idling around on the ramp, and taxiing at lower power settings the prop is on it's low pitch stop and the governor has no effect on RPM. So, any power changes will cause a change in RPM.
If you are at low power settings (1000 RPM) on the ground, you can move the prop control throughout its range and it will have no effect on RPM or MP. Next time you are out, try it. Just don't pull it into the feather detent.
"During Runup - Pull back prop control, MP pressure increases (why not decrease?)"
Because when you reduce the RPM, you are sucking less air through the same sized opening. This results in less vacuum in the intake manifold, which equals a higher MP. The same thing will happen in flight, so you might want to revise this one:
"Air - throttle is used to change MP, prop control is used to change RPM"
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