The StuRa comprises of representatives from all 51 student councels as well as elected representatives from political lists (Hochschulgruppen). The political lists may hold up to 50% of the seats depending on the turnout of the university elections (which is usually rather low, though). The StuRa seats every two weeks and sessions are public, but usually held in German. However, every student has the right to put forward a motion and speak before the StuRa. It decides on various matters such as finance and the composition of committees, and discusses issues from all aspects of student life in general. Every student pays 7,50 € per semester to the VS, from which a part is distributed by the VS itself and another part by the student councils.
A current list of our representatives in the StuRa can be found here.
The RefKonf also seats every two weeks and takes care of more specialized issues, such as ecology, public relations, culture, traffic and mobility, etc. If you have a specific issue you want to address or a specific project, then these are the people to speak to.
For issues concerning international students, you may want to refer to the RefKonf brach for international students. The StuRa also has a helpful page about tuition fees for international students, which you can find here.