Should Saul have Killed Jonathan? - 1 Samuel 14

In 1 Samuel 14, we see Saul make a rash vow, putting his men under demands that didn't require, nor command. As a result, his son Jonathan's life is on the line as he unintentionally breaks this vow. The two questions arise from this passage - 1) Should Saul have followed through with his vow and killed his son, Jonathan, for breaking it? and 2) What is the lesson this passage teaches us?