I'm in Germany at the moment with a 90 day tourist visa and my question is very simple, can I sign up to a German Language Course and get the visa changed so I can start right away? Or I have to go back to my home country and apply there.
Generally speaking, it is necessary to apply for a student visa before entering Germany in a country where you have your usual place of residence (not necessarily your country of citizenship but definitely not a country where you are staying with a short-stay Schengen visa). A switch is not possible.
There is an exception for citizens of a small number of countries (USA, Canada, Japan, Australia, New Zealand, Israel, South Korea and, with some restrictions, Brazil, El Salvador, Honduras and some European micro-states…) who can in fact apply for a residence permit even if they entered the country without long-stay visa but those are countries whose citizens do not need a Schengen visa for short stays either.
Colombian citizens definitely need to apply for a student visa from outside Germany. And I am not sure a “language course” is necessarily enough to get such a visa (it seems mainly intended for a full programme at a university).