"Irregularities" in neighbors' boundary construction ... Tips

No, only if the neighbor had wished to conceal his illegal unauthorized construction, according to the statement of the employee of a public authority. I have now understood that this is inappropriate.

Is the employee of the public authority from the wastewater association? What does it matter to them whether there is/was a building permit and how should they know that? What would you do if an employee of another public authority (e.g. registry office) informs your neighbor that you are building the whole house without a building permit? Only the building authority (or whatever it is called in your area) is relevant here.

Well, it’s 30 cm that I’m already missing,

I don’t see the 30 cm on your property, at most in depth. Next time with a scale, please :)

I don’t understand the question regarding the period of origin.

Well, it was obviously already clear to you during your house and carport planning that something was there.

because the above-mentioned employee said so

The wastewater employee surely means the illegal water disposal. He has no authority to judge anything else.

and in case of a sale the brown hut will be removed.

Why should a buyer of the right property remove the canopy? He is buying it with it. Unless it bothers him or he doesn’t like it.

I don’t know if the "dark brown carport/covered parking space construction" is allowed to be extended if we currently accept it."

Do your neighbors know whether you might possibly extend your carport? I find that a bit far-fetched, especially since there is a greenhouse there.

that a possible future buyer might turn the "dark brown carport/covered parking space construction" into a sauna, lounge, party room, or something similar

No, not allowed.

My husband and my sister-in-law already find me too "pushover,"

Well, I can already see you apologizing to the neighbors a thousand times in advance before the question arises whether the plant, the branch, the stone, or who knows what is 3-4 millimeters too close or over the border. YOUR plant, stone or branch, mind you :D

Thank you for the link. I still do not see the 30 cm on your property. It looks as if it goes 30 cm deep and outward, so there is not a significant widening of the foundation towards you. (Maß geraten anhand der Gräser) Correct me if I am wrong. Nevertheless, a ruler would be advantageous.