As mentioned before, the egr valve is closed at w.o.t. - so there's no performance benefit to removing it or having it be non-functional; however, if you have to retard timing to stop the pinging, that can hurt performance. So, there may be a benefit to having the egr hooked up unless you turn off the egr function in the computer with a chip.
The air injection works as your mechanic friend described - excess oxygen is required for additional oxidation to occur after combustion has occurred in the chamber. The chemical reactions that the cats speed up need excess oxygen to occur. The O2 sensors will still, however, read the exhaust stream, and when you're in closed loop, they'll help the computer adjust the amount of fuel injected. At w.o.t., the engine goes back into open loop, and it ignores the O2 sensor readings anyway - the so the lack of excess air being injected is a non-issue performance-wise. One of the most common 'mods' out there is either removing or bypassing the air pump - and folks hardly ever report any drivability or check engine light issues. The computer will throw a diagnostic code into memory related to the malfunctioning components - thermactors - but it doesn't seem to harm anything. Unless, of course, you have an emissions test to pass.