EU-citizens do not need a visa / residence title for specific purposes, if they would like to stay and study / work in Germany.
Students from countries outside of the EU should consulate with the embassy of Germany in their country of origin regarding a student visa application. Please take in consideration that all visa applications take time to process.
Visa applications must be made by the students, for any advise or further information contact us at the FAAC we will do our best to help you in the process.

Here are some links that might shed some light on your questions:

What is the Schengen Visa and how to apply?

What are the costs living in Germany? And can i get a student working permit?