"direct experience by judge" sounds like a can of worms. What if the judge believes religion is real based on their "direct experience", in a blasphemy trial?
In English common law, this is called "taking judicial notice".
It's usually for common-sensical things that aren't controversial. Of course, judges could misapply this rule, but if a judge is sitting on a blasphemy trial you have more problems (with the legal system) than a dispute about whether "religion is real".
I suspect the rule is just to make things less "anal" for court procedings. Otherwise every small bit of fact needs to be proven. Things like "summer is hot", "Taylor Swift is a famous singer", "computers can be hacked", "smart phones can take photos", etc. etc. Surely you don't want to call expert witnesses for these, right?
And given that the judge ultimately calls the shots (since they're the ultimate interpreter of the law), you'd have a problem if a biased judge is appointed anyway, no matter what rules of evidence is adopted.
I don't know a good translation for "Inaugenscheinnahme". Literally "taking-into-eyeshine".
It means observing the accused, the witnesses, objects introduced into trial and so on. In the sense of experiencing something with one's senses. It does not mean "let me apply my world view".
Visual inspection by the court, Sections 371-372a of the Code of Civil Procedure
This consists of any direct, sensory inspection by the judge for evidential purposes. Contrary to the somewhat misleading term used, ‘Augenschein’, ‘visual inspection’, it may also include sensory inspection by touching, smelling, listening and tasting. Consequently, sound and video recordings and data storage media are also included.
I suspect that's so they don't have to prove obvious things like: cameras exist, cameras can take pictures etc. Or for stuff like the defendant attacking someone during the trial.
[Edit: Interesting replies, thanks!]