What's the relation between TAS and Mach in tropopause? I understand that TAS decreases with altitude with constant Mach number in troposphere, however I'm not sure what happens in tropospause, as the temperature is constant, however the density is still decreasing. Does that mean the TAS will continue to decrease, just at a slower rate?
The speed of sound depends only on air temperature, not density. So, for a given temperature, a given Mach number will always equate to the same TAS.  

In other words, for a given Mach number, TAS remains constant throughout the constant-temperature region above the Tropopause (ie. 37000ft to 65000ft in the International Standard Atmosphere, ISA).