How do you determine what ending 'ciekawy' should have? I thought it would be - y here, but it's -ie?
It's an adverb not an adjective. And it describes how the student speaks or rather should speak. It does not say what the student is like.
Is it possible to change the order of words in polish? Chy ciekawie mówi ten ucheń? Dzięki!
It is posiible. I do not think I would ever say that, but in a poem or a novel it would be ok.
("czy ciekawie mówi ten uczeń?" it's cz in Polish where it's "ch" in English.
When do you use student vs uczen? I just now learned there is an alternate word for student.
"Uczeń" is for primary/middle/high school. Then he becomes "student" when he starts university education.
How can to tell from the English context that this is uczen and not studentka?
You can't, especially that in American English, as far as I understand, "student" is used for both schools and universities.
So there should be four possible interpretations, depending on the level of education and gender.