Q: (Interactions):
"My model includes X1 and an interaction between X1 and X2. Do I have to include X2 as well?"

A: Although it is conventional to include X2, there is no mathematical requirement to do so. You have to think theoretically about whether a main effect of X2 is plausible. Below are the statistical consequences of making an incorrect decision.

If X2 has an effect which you omit, the omitted effect will bias the interaction, as well as other variables that are correlated with X2.

If X2 has no effect and you include it, you won't have bias but you may have some needless collinearity between X2, the interaction, and other variables that are correlated with X2.