BOAC,
Forgot to answer your first question.
At a constant Mach climb TAS decreases.
Here is where I get confessed, I know I should accept this but I want to understand why.
Both Mach and TAS increase with altitude, so the only thing that make sense to me is that Mach is increasing in a faster rate than TAS and thats why TAS is decreasing in a constant Mach climb.
Thank you for taking your time and helping me with this!