One thing to consider is that N1 is just RPM. N1 x Density gives thrust.
True.
(i) EPR is thrust.
Not true. EPR is Engine Pressure Ratio, in other words exhaust pressure divided by inlet pressure. At altitude, inlet pressure (i.e. density) is lower, and at a constant EPR, exhaust pressure is reduced by the same percentage.
Some engines may have EPR "bumped" at altitude to compensate, to maintain thrust equivalent to SL; So the thrust/EPR relationship DOES change!
Years ago, a Pratt engineer told me a 1% error in N1 equals approximately 3%-4% error in thrust output, while a 1% error in EPR equals a 1% error in thrust. That is, EPR is a measure of thrust, but N1 is a measure of fan speed.
I think most engines will have a 2.5 : 1 relationship between thrust and N1.