What questions would you like to see on an NCO Academy Pre-Test?

I think the most effective NCO's and Staff NCO's are those that understand effective communication techniques, leadership traits, and how to be an effective mentor. They should also know how to evaluate performance, and should understand the disciplinary process. Your questions and training should center on those things.

Without involving disciplinary powers, How would you motivate a small unit (squad ect.) that has lost confidence?

What are the basics of effective communication? How important are they?

Army Programs

Mentoring

Evaluations

Scenarios pertainjng to suicide, death in a Soldier’s family, sexual harassment/assault, etc. Answers require a logical sequence of actions and Army resources available to the Soldier AND the Army leaders thar pertain to the situation. This is definitely most practical and things that I would hope NCOs know.

First off should be their job and all skill level 1 tasks. Counseling should already be good because they've been getting counseled for years. They should be taught how to support their soldiers and how the army works. How to request a school, how to enforce regulations. How to advise an Officer/senior NCO that they are incorrect about something, what their PDM says, what advanced programs and application jobs the army has, show them that they need to check their mail.mil at minimum weekly.
BLC doesn't teach leadership (no army schools do) it just teaches things a SGT does, like the popular "read from this overused PowerPoint deck and call it teaching/training" or "this is how to make soldiers conduct ineffective PT"
Leadership is an individual thing, because subordinates are all different. The courses should teach more interpersonal skills, discussion techniques, conflict management, etc to allow a leader to cater their style to the Soldiers in their charge.

TLP

Readiness is a must to understand. At the E5 level they might not need to understand specifics of hot to get to readiness but understanding the principles and how training events, schools, and other command objectives get to readiness will help them communicate to their Soldiers the "why" a task must be accomplished.