Smithgd,
That's about perfect, which one slight addition. In senario 1. "If the pilot can carry PAX", then it doesn't automatically mean that the pilot being checked out logs P1 and the instructor nothing; it simply means that that is an option open to them.
It could also be that the instructor logs P1 and the pilot being checked out logs either Pu/t (if they get some training) or nothing (if they don't get any training). It's really about what
they agree to before they go flying 
But other than that, I agree 100% with your summary.
dp