They both are used as drink, but beber is used for liquids and tomar includes other senses (like take). Tomar o ônibus, tomar banho, tomar remédio.

Because if it were THE students it would be OS estudantes

"take" used to mean "drink" has become rare in english, and is usually avoided when the alternative meaning of "pick up and hold onto without asking" is a possible alternative meaning. One does still say "I take coffee with my breakfast," or ask "do you take coffee or tea," so arguably, it should be accepted here.

Here we don't have an article because we're talking about students in general - it's a habit/fixed behavior of students (or so Duolingo thinks). "The students" is a specific group of students.