(a) The operator will do the sums to determine the desired numbers.
Once you have decided on the climb/descent Mach and CAS, the changeover level falls out of the Mach equation ... which is what you suggested earlier.
if speed of sound is a fn of Absolute temp, then so will be the tas value for .78
Absolutely,
a = a0 √ [T/T0],
so OAT determines the speed of sound and then
TAS = M a
but the OAT has naught to do with Mach.
(b) Looking at an earlier post ..
Just wondered why did they put the end of using Vmo at FL24600 and the start of Mmo at that level isn’t it an indication that this is the trasition altitude between switching??!
Exactly .. Vmo is a specific speed and Mmo a specific Mach Number. Define the two and the equation defines the changeover level for that combination of Mach and CAS.