What exactly is engine design speed? Any further information is welcome, this is what I have learned so far:

Engines are designed to operate at a certain RPM (N1). The compressor consists of small 'wings' which are fixed in position, so the angle of attack will vary only by engine speed and forward speed. The engine design speed should be 85-95% N1 for most turbofan engines, this results in an optimum airflow through the compressor. Above or below a higher risk exists for an engine to stall.
Engine design speed is the shaft RPM and vane pitch which yields the rated thrust that the engine was originally intended to furnish. This will typically be quoted for takeoff at or near sea level at a standard ambient temperature (including a time limit to control maximum temperatures inside the engine) and for optimum cruise conditions at altitude (which will include specification of nominal fuel burn rate in pounds per hour).