First, indonesian language has no past tense. Did or do must be correct in the same logic.
And articles, is it wrong to put "the" before the objects "students" and "teachers"?
You are absolutely correct in both cases. It sounds more natural if you put "the" in front of students and teachers.
It think it has past, not with the verb, but with particles!
kata influence mestinya juga bisa dipakai
persuade juga bisa digunakan untuk kata "mempengaruhi"