A sharpened pole was a common execution device (see also Esther 2:23; Genesis 40:19, 22; Joshua 8:29).
Seventy-five feet (fifty cubits) is very high, but Haman wanted to make an example of Mordecai, allowing everyone to see his body. The number might be an exaggeration for effect—fifty cubits is a round number—or it might mean a stake placed high on the city wall for public viewing.