All conventional EGR systems I've looked at have the EGR valve located downstream of the throttle. The exhaust gas is an inert diluent and has only a secondary effect on power. The effects of adding EGR while holding power constant will be: the manifold pressure will rise, as will the charge temperature, throttle may have to open slightly to flow the same amount, due to the reduced vacuum; indicated power may go down slightly due to slower combustion, but this will be offset by the reduced pumping loss and can be further offset or even negated with increased spark advance, so thermal efficiency will normally increase with a well calibrated EGR strategy versus non-EGR. This applies to part throttle. At WOT EGR will displace combustible mixture, reducing power. EGR is typically not used at WOT on spark ignited passenger vehicles.
To answer the OP's specific questions, manifold pressure will rise, total mass entering cylinders will rise, fresh air mass will go down slightly due to reduced vacuum. This will cause a drop in power unless throttle is opened and spark timing is advanced as explained above.
Assuming your vehicle is equipped with a 3-way catalyst, far more likely reasons for high NOx are marginal or failing closed loop control, or a failing catalyst.
Retarding timing will actually reduce engine out HC along with NOx. The reason is, with retarded combustion, the effective expansion ratio is lower, which results in higher temperatures late in the combustion cycle; allowing more time for HC to be oxidized; in addition, the higher exhaust temperature provides better oxidation in the exhaust system.
