Does an engine's EPR naturally tend to decrease or increase with rising airspeed during the takeoff roll and up to 400' (higher pressure at the front means a lower EPR?) or does more air into the engine improve the efficiency of the engine (= more thrust). My only experience is from engine ground test runs. Some adjustments cannot be carried out on the engine if the windspeed is above a certain value.
Short answer is "it depends". Some engines will increase EPR (or N1) with increasing speed, some decrease (the old hydromechanical controlled engines nearly always decreased, hence the term "lapse"). I know the PW4062 EPR would increase between 80 knots and 250 knots, I don't recall about the RB211. The nice thing about "lock and lapse" is it's consistent, so the performance is easily predicted.
I assume you mean the thrust lever position EPR command (not the FMC-generated limit set during the preflight).
Yes... The FMC 'bug' on the EPR tape is usually referred to as the EPR target (you'll also get an EPR limit - the max rated EPR for the conditions). EPR command is the line that moves immediately with throttle movement, then the tape 'fills in' as the actual EPR closes on the EPR command. EPR command is always dependent on the throttle position (with the exception of the small FMC 'trimmer' signal I referred to earlier), and the FAFC/FADEC will do it's best to close loop on the EPR command (note, near idle, the engine is being controlled to N2/N3, not EPR, so EPR command is automatically set to EPR actual since EPR command is basically meaningless when the engine is being controlled to a rotor speed).