we want to apply there to be student는 안되나요?

That will be "우리는 학생이 되기 위해 그곳에 지원하고 싶습니다" I think it is quite different

앞의 We 때문에 students 가 되는것 같아요

We would like to apply to be students there.

Students 복수형태가 맞나요?

We want to apply to be a student there. 로 Student가 맞지 않아요 ?

we는 복수니까 student가 복수가 되서 students가 맞습니다 !

apply for its students

we'd like to apply to be your student

We wanna apply to be students there.

We want to apply to be students there

We want to apply to be students there.