In Germany all people have to provide first aid - no matter where the accident has happened or if they are trained first aiders or not. The first aid training does not change the legal status: Trained first aiders do not bear liability for damages or wrong done first aid. On the contrary they are eligible for full refund of all expenses or suffered damages.
However, as a trained first aider you will be much more competent in offering first aid. It is not everybody's cup of tea to do a first aid training. But it would be nice, if this is a mission for you. Unfortunately at the FU first aid trainings are only offered in German language. Please see the information of the Weiterbildungszentrum. Only people with an employment relationship may get a first aid training. This includes also temporary contracts like a student tutor or doctoral candidates.
If you are a trained first aider the staff in your work environment should know this. A good idea is a notice at the door of your lab.