Yes, PCO2 of the BLOOD determines breathing, not PCO2 of the air. The air we have is pretty high in O2 (about 21% of the air which at 1 atm gives PO2 a value around 160 mmHg) and low in CO2 (about 0.04% of the air which gives PCO2 a value around 0.3 mmHg). If you go to a lower altitude the PO2 increases along with the PCO2, but since the PCO2 of air is pretty close to 0 anyways, it doesn't make that much of a difference, but you get a higher amount of PO2.
The second question is a physiology profs favorite. Your body will make more red blood cells at higher altitudes (PO2 determines hemoglobin saturation so with a lower PO2 you need more hemoglobin) to combat the lower amount of PO2 in the air. It's why some long distance athletes (cyclists are notorious) will do (or at least used to, now people will just extract blood and then wait for the body to regenerate it and then put the blood back in {look up blood doping}, but that can lead to a clot) high altitude training so that the body will make more blood cells and then right before the event, go back to the right elevation so the body doesn't have time to adjust and get rid of the extras and you have more available O2.
A more likely topic for the MCAT is the hemoglobin disassociation curve ()
