Is this kind of number used for counting, like "one student, two students..." or to specify a number, like in "I see a student"?
it is also used as in "a student" (unspecified - some student) - Одна студентка сказала, що викладач злий - A (some) student said that the professor is angry
Yes, it is a number. There is no either indefinite or definite articles in Ukrainian
We dont use articles in Ukrainian