Aspirin is fine. But will do nothing for high RBC/HCT. A blood pressure monitor is a great tool to have on hand and use. However, it is not a replacement for blood work. You won't know if you have high hematocrit with a monitor. I had decent blood pressure reading at over 50% hCT (a good place to donate)
I have no idea where you got the idea that a cut would not stop bleeding. We'd all be dead by now.