The post of our driveway gate protrudes about 10 cm onto the neighboring property

The really tragic thing is that the new neighbor (represented by his architect) behaves like a bull in a china shop right at the beginning of the new neighborhood relationship - perfect conditions for a long-lasting conflict. Those are great prospects... I also made a few mistakes at the beginning regarding informing my neighbor ("involving" him about planned construction measures - it would have been much more relaxed with a bit more notice)... but here it is clearly much worse. I would be very interested to hear how the matter develops - please provide an update if there is any news.

A 1.5m high wall is quite a statement. Is that even allowed? (Bebauungsplan, Landesbauordnung, Nachbarschaftsrecht...)

That is property damage and theft. If he messes with you again, reserve the right to take legal action.

I understand your position and even share it, but wouldn't the fence be the neighbor's property if it actually stands or stood on their side of the boundary line? Just hypothetically ...

but wouldn’t the fence be the neighbor’s property if it actually is or was on their side of the boundary line?

no! The landowner could at most demand its removal.

Just because I illegally park my vehicle on your private parking space doesn’t mean it belongs to you or falls under your control.

The following applies here:

Bürgerliches Gesetzbuch (Baugesetzbuch) § 1004 Beseitigungs- und Unterlassungsanspruch (1) If the property is impaired in a way other than by deprivation or withholding of possession, the owner may demand the removal of the impairment from the intruder. If further impairments are to be feared, the owner may sue for injunction.

but wouldn’t the fence belong to the neighbor if it actually stands or stood on their side of the boundary line?

Yes, if no one can remember anymore who originally built the fence. But if at least one of the neighbors assumes that it is their fence, either because they built it themselves or because the previous owner told them so, clarification is necessary.

If a property owner, as suggests, goes looking for boundary stones themselves and finds things they believe to be boundary stones, and their neighbor doesn’t care at all, and the owner erects and pays for a fence themselves, then the fence does not become the property of the neighbor just because they were not boundary stones or were incorrectly positioned and therefore the fence is now completely on the neighbor’s property.

but a boundary stone is a boundary stone is a boundary stone

but not every boundary point is marked, and certainly not by a boundary stone. And even in cases where this is so, it is not certain whether the boundary stone is still where it is supposed to be.

but not every boundary point is marked and certainly not by a boundary stone. And even in cases where it is, it is not certain whether the boundary stone is still standing where it is supposed to be.

Correct. By far not every one. You do not know the local conditions and neither do I. For this reason -> look for boundary stones. Then determine if they are where they are supposed to be. One step at a time.