Leute, ist das Schimmel?

It looks like mold to me. Do you know the humidity in there by chance? First photo looks like a water leak; can’t tell if old or active.

I’d move out if I was renting; if you can see it you’re only seeing the tip of the iceberg and the correct remediation (for the landlord) is costly and time consuming. Also can be detrimental to your health if you have a weaker immune system.