Space between garage and neighbor

It depends on how much space you can leave on this side. A few centimeters are not enough to plant something there, repair something, etc. So either you can leave a nice piece free and also design or access/repair this area accordingly, or I would put it directly on the boundary. In any case, better a few centimeters further away from the neighbor than a centimeter over, and make sure that I do not "burden" the neighbor's property. Whether moisture etc. plays a role there will also depend on the neighbor and what he does on his side at this spot. Our garage or carport will be directly on the boundary, and the neighbor can do whatever he wants there; we agreed on that right from the beginning.

First of all, thank you for your tips. Instead of planting, we planned a drip edge as a strip. Nothing was supposed to grow there and it also protects against rain. If I go right next to the fence, the wall has no protection, right? So if I understand you correctly, either a gap wide enough to walk through or directly up to the boundary.

I would definitely NOT make a "gap." The neighbor could rightfully possibly build their structure directly on the boundary, and then you would have a dark corridor where you can hardly get through. So either a comfortably walkable width (wheelbarrow, handling tools, etc.) or directly on the boundary. I also don't find a half-measure visually appealing. Clearly intentional distance or none at all.

As far as I know, a garage is only permitted as a boundary construction if it is placed exactly on the boundary, right? Our garage looks pretty ugly from the side. But I don't care at all because only the neighbor sees it.

If you were my neighbor and asked me, my answer would be that I would prefer to look directly at your garage wall rather than a leaf collection corridor; I would remove the fence along the length of the garage.

Regarding 1) The garage has no roof overhang on the side.

That speaks in favor of building on the boundary.

Regarding 2) The property allows a shift of up to 1m away from the neighbor’s fence.

That speaks in favor of a 1m distance from the boundary.

Regarding 3) The neighbor has a fence there.

That speaks in favor of a boundary distance. Sensibly as much as to allow passage, in my opinion 1m. The question is whether he plans anything else there in the foreseeable future, e.g. a garage, which would speak again in favor of building on the boundary.

Regarding 4) No idea, that’s why the question.

That speaks in favor of a boundary distance.

Regarding 5) We don’t know each other yet

see

As far as I know, a garage is only permitted as a boundary building if it is built exactly on the boundary, right?

In some federal states you either have to build on the boundary or maintain a minimum distance, e.g. 1m in HE and NI, 0.5m in BW, in others the distance is optional, like for the OP (ST) or for me (NRW). I find the one meter sensible though.