What is it that even the most competent of

What is it that even the most competent of students occasionally stumbles over a seemingly simple question, and finds himself/herself unable to determine the correct answer?
Everything ok in the above sentence?

You need some changes:

Why is it that even the most competent of students occasionally stumble over a seemingly simple question and find themselves unable to determine the correct answer?

You could use ‘finds himself/herself’ as well, but as the plural will work here without a significant change in meaning, I would suggest that you use it as it provides a much neater solution than to use ‘himself/herself’.

What is “competent of students”? I think it is a quality. If then how a quality stumbles over?

I have also another question that is why not “s” with the stumble?

‘competent’ is an adjective to describe the ‘student’. A student can ‘stumble’. In this case, it is a metaphorical stumble.

‘Stumble’ is correct because ‘students’ is plural.
singular: he/she stumbles
plural: they stumble

You mean the verb of stumble is “student”?

I am not clear about the use of “it” in this way.
Bev, Could please explain it to me with some example?

I’ve already corrected the use of ‘what’.
It should be:
“Why is it that even the most competent of students…”

You can read it like this:
Why is it a fact that even the most competent of students…
Why is it the case that even the most competent of students…