All the places I search, it says that for internships there is a seperate visa. My question is, would I, as an Indian student, be able to intern on the student visa?
An internship that is mandated by your study program’s statutes, i. e. necessary to graduate: No problem, 16b (1) 2 AufenthG, 16.0.5, 16.3.5 VwV‑AufenthG. (Well, almost no problem, but I presume you are an honest person.)
Internships not required for your studies: This is assessed on a case-by-case basis since the contracts differ in wording and thus the legal nature of the business relationships differ, too.
In principle it should not affect your study’s successful completion (e. g. with respect to time) and the primary purpose of your stay remains for studies (e. g. the compensation, if any, is not too big).
I cannot name you any figures, but the margins are greater if the internship is officially recommended by the college you’re attending.