Which jobs do I need certificates or “Approbationen” for? Is there a boundary between jobs that you need “Approbationen” for and other jobs?
Yes there are for example when you want to become a doctor and open a doctor's practice you need to have an “Approbation”.
Basically you need certificates for most of the jobs in germany. May it be lawyer and notary or a judge, teacher, craftsman and scientist. Therefore we have all these "Ausbildungen" (apprentiships) and University degrees in Germany.
The jobs you don't need certificates for are: housekeeper, assistant on a construction area, waiter and service in the gastronomy sector.
You are also free to become whatever you want when you work in the creative sector. You can become an artist, painter, designer, photgrapher, writer, musician and singer without having a degree or certificate in it.
Especially in the start-up sector you have great possibility to work in high positions even without degree, because you do something where there is no education for, yet! Especially working in the internet and inventing some new software or creative business models can be a good job opportunity.
Here is a list in german for which jobs an approbation is needed. It is needed for the so called "Heilberufe" so jobs where you heal a person or an animal. (anwalt.org/approbation/#In....)
To decide who can get an approbition, there is a "Approbationsordnung" from the ministry of health in germany, so for all the regions in germany there are the same laws.