For the first question, there is no particular term for X. Exclusion crteria is a term used to refer to rules used to exclude patients from being enrolled in the trial. There may be an analogy here to the process of excluding data when a mathematical condition exists but it is a different situation and I have never heard the term exclusion criteria used in that case.
In my experience with clinical trials the analysis you are describing in the second question is most commonly called subgroup analysis. I imagine the epidemiologist use that term also.