Airspeed does not increase with altitude. Rather the air density decreasing, you will have to increase speed to obtain the same lift (at a given AOA). Therefore your indicated stall speed increases.
If you could put your eyes on a CTM graph (simple graph from ATP theory) referred to as Chicken Tikka Masala, shows how speed and Mach change with altitude compared to one another.
Rest of the question, not familiar with Concorde, but above the tropopause, the temperature moves very little, so no change in the MN for a given TAS, but increasing the altitude would still benefit for fuel saving.