Yeah, it sounds nuts to us, but it was common in the ancient world and was designed to keep communities together. A messy business, that's for sure.
A woman who tries to help her husband in a fight and strikes another man below the belt will have her hand cut off. So much for self-defense class.
Be honest. Don't use false weights. (They're talking about the weight of grain or the volume of olive oil, or even the measure of precious metals like silver and gold.)
Punish the Amalekites for striking down the weak among you. The Amalekites are the perpetual enemies of Israel. Several passages in the Bible speak of annihilating these guys (see Numbers 24:20, 1 Samuel 15, 1 Chronicles 4:42-43).