A. Yes.  Checking the Eligibility Checkbox at the top of Form 1023-EZ is supposed to mean the applicant organization is not applying for status as a church, a school or a hospital.  Question 12 of the Eligibility Worksheet asks about churches, question 13 asks about schools, and question 14 asks about hospitals.

This question was new in the 1023-EZ dated January, 2018.  Apparently, so many ineligible organizations were filing Form 1023-EZ that the IRS saw a need to duplicate the church, school and hospital questions.  

Q. Doesn't the Eligibility Worksheet already
ask about churches, schools and hospitals?​