-MEC will schedule FF to get the desired N1 using Thrust levers position.
How does the PMC work?
In the fuel circuit, why some fuel is diverted and reheated after the second stage pump? Is that for keeping enough fuel to the MEC to make sure priming is ensured?
The MEC is a hydromechanical device that will control to a fixed N2 (at a given throttle position). However thrust is N1, and the N1/N2 relationship will change with altitude, airspeed, and the thermal condition of the engine. On the 737, the PMC is an analog computer that provides a trim signal to the MEC to help maintain a constant N1 (on the 767, the PMC was a digital device, but the intent is similar).
The second (high pressure) state of the main engine fuel pump outputs considerably more flow than the engine needs - there is a valve that bypasses the excess fuel back to the intake side and maintain the desired pressure in the MEC.
BTW, Wing Anti-Ice is a real bleed hog - it takes a lot of air. Since 'conventional' icing (super-cooled droplets) doesn't exist above 30k (at least according to the regulations) the bleed system isn't sized for it. The icing threat above 30k is "Ice Crystal Icing" or ICI. ICI won't adhere to cold surfaces (it just bounces off) but it can melt and refreeze when it hits warm surfaces (which has been a big problem for the engines).