Abstract:
In Germany it’s complicated and it’s best just not to get into trouble
Full text:
In Germany a unicyclist is, legally speaking, a pedestrian. Just like rollerbladers and riders of kick scooter… they are all categorised as “sport devices and toys” -> pedestrians.
This means that if you ride on a road outside town with no pedestrian path or anything along it, i.e. an ordinary country road, the law would actually require you to ride on the very left side rather than on the right like a cyclist 
I use the subjunctive because in real life of course nobody does that.
But if you fit all equipment to your uni that the law abbreviated as StvZO requires bicycles to have, you count as a cyclist. Wolfgang “Yeti” Schaper found this out by inquiry (German).
You speak German, so you can easily look up what these requirements are. It’s a lot and it includes dynamo lighting. For the brakes, one is enough for anything with a fix gear.
Most cyclists don’t care about StvZO compliance. None of the unicyclists do (thus accepting pedestrian status). Most policemen don’t either, they are satisfied if, when it’s dark, a vehicle emits white light at the front and red light at the rear. Which is what bikes’ technical requirements read like in countries with more sensible road law in this department.
But a court of law will care, if you want to claim vehicle status because you rode like a cyclist (∈ vehicle) 
That’s what makes our legal status here unsatisfying.
We keep our heads down because we agree that if anything about it changes, it will certainly change for the worse.
To get even more confused, see this thread (German).