Build a 150-160 sqm single-family house in the parents' garden - overwhelmed!

Have you already checked the land use plan to see if the property is in the outer area? Possibly check in the geoportal of the BL. Or specify exactly where the property is here.

We have already received feedback from the building authority that it concerns development according to Paragraph 34. Therefore, it is not an outer area :) The land use plan says residential area.

That doesn’t necessarily help. We have the same situation in our town with one of the last garden plots with its own parcel number. Theoretically, it could be an outer area within the inner area. How the boundaries actually run has often not been precisely surveyed in unplanned inner areas, or the boundary lines from old plans were transferred to the geoportals without being checked. Only the responsible building authority can help with that, and often this is possible without a formal building pre-application.
Edit, the response overlapped :)

That doesn't necessarily help. We have the same situation in our town with one of the last garden plots with its own parcel number. That could theoretically be outside area within the inner area. How the boundaries actually run is often not exactly surveyed in the unplanned inner area, or the boundary lines from old plans were adopted in the geoportals without verification. Only the responsible building authority can help here; often this also works without a formal building inquiry. Edit, the reply overlapped :)

What exactly did you mean by "that doesn't necessarily help?" :)

Of course, we would like to build as close to the street as possible in order not to waste the garden.

First, separate yourself from this idea.
A) You also need space in front for parking, cleaning bikes, go-karts, buffer to the street, …, b) there is no waste, because space is needed everywhere, and c) the house should be planned according to the floor plan and the light incidence in the house.
The garden itself is a manually created green area, so the front garden can also be planned.
Unfortunately, I cannot load the two pictures, so I cannot see where south is in the pics?
But keep in mind that others are not stupid and have no idea. There is usually a reason why it is built that way.
For infiltration, you go to the water department.
Then you take graph paper and consider an approximate floor plan. You think about where the garden would make sense. (I would probably create a west garden on that plot), then you submit a building inquiry with the sketch, then a soil investigation report.

First separate yourself from this thought. A) you also need space in front, for parking, cleaning bikes, go-kart, buffer to the street, …, b) there is no waste, because space is needed everywhere and c) the house should be planned according to the floor plan and the light incidence in the house. The garden itself is a manually created green area, so the front garden can also be planned. Unfortunately, I cannot load the two pictures, so I cannot see where south is in the pics? But keep in mind that others are not stupid and have no clue. There is usually a reason why it is built that way. For infiltration, go to the water-things place. Then take graph paper and consider an approximate floor plan. Consider where the garden would make sense. (I would probably create a west garden on that property), then a preliminary building request with the sketch, then a building ground survey.

The garden lies to the south ;) the neighbor’s house borders to the west. Parking is included. Carport is already available. We are getting it from my father.

What exactly did you mean by "that doesn’t necessarily help?" :)

the view into the geoportal or the land use plan to reliably determine boundary lines.