1 - It was my understanding that the ALT was calibrated with respect to ISA pressure lapse rate. When density or pressure are higher the ALT will over read.
That's incorrect. Remember, the pressure you set in the Kollsman window is the datum above which the altimeter reads pressure and thus altitude. So if you wind it down below actual pressure, the alt 'thinks' the datum is at a higher altitude, and that the plane is closer to it, so the alt shows a lesser than actual height - or
underreads.