Since the last one is the easiest I'll start there
The question being discussed did not ask for VX. It asked for the bast rate of climb speed (VY).
For max ROC (at VY) we must have maximum excess THP
that will occur at the highest TAS, because you can't have a speed that gives a lower drag Coefficient in order to increase THP TAS must increase for constant power; of course the power setting will be lower for level flight than climbing flight,..but the maximum excess thrust in the case stated still should occur at Vimd as both thrust and drag decrease together in a climb
but a piston/prop is not a constant THP machine. And in determining best ROC it is the excess THP that matters.
that is true because TAS. rho, and AoA i.e induced drag will be changing,..but generally Vy is only one tabulated speed, but constant power implies that the product of T*V remains constant,...although that is an idealized situation
so as you stated
So having minimum drag will not necesarily give you maximum excess THP available.
The text that you have quoted apears to be more concerned with how VX and XY vary with changes in altitude.
that's not the text, that's one of my boring rants on Pprune
now, I'm not really a morning person so I make no claim that I have not put some horse hooey in the mix,..but I try
