My findings on the Andromeda's Eye telescope are as follows:

Objective Lens, Star Diagonal, Eyepiece - Working as intended.

Optical Tube Assembly - Working as intended, but dusty. Should we send a student to aid in cleaning...?

Mount - Error detected. The Telescope does not move horizontally or perpendicularly.

Focusing Components - Working as intended, though they cause me great misery nevertheless — Seeing as they can only reveal the constellations directly up ahead.

Conclusion: Consider conducting a proper maintenance routine.

- Professor Androme

During my absence, I expect you, my young star explorers, to consider the following assignment! Solve it to lift the seal — and to earn a good grade!

Imagine your life as a circle.
It can be a halo, bright and hollow — or an interlocking chain; an oroboros. Mind you: The emptiness, the vastness in between, is valuable. It serves as a canvas upon which we may draw our constellations and mark the flow of time, separating what is from that which isn't.

You spring from the inside of the circle — poof, there you are! A novice, young and spry, undulating along the proposed curvature, aging into elderhood and falling to ash before sprouting anew.

Your task: Use the telescopes on the balconies to discover where, on this eternal cycle, our beginning and our end must lie!

To the left, I want you to find our origin — where we were plucked from the void and thrown onto the canvas. The point of our creation!

On the right side, focus on where we rest — the hearth that rekindles our ashes!

I await your results with bated breath!
- Professor Androme

The master's riddle is a tedious one... A circle has no end, nor beginning! Though the more I think on it, I begin to see all the hints he strew between the lines... in the empty space below, on the canvas, so to speak!

So my theory is as follows:
As Ancients, we all spring from the Mother Flame... but strangely, only one of the telescopes can be pointed towards where she resides. Perhaps part of the riddle is meant in a less literal way? Does the master refer to an "arrival", rather than a birth?
I think his remark towards "creation" could prove valuable...

I'll try my luck with the telescopes and see!