What is the house ground
The house ground is the "three-dimensional floor plan" of the building. Through it, sections are made and submitted as construction templates, e.g. the ground floor plan, which is a horizontal section through the house ground, 1m above the finished floor level of the ground floor. Thus,
the spot that intersects the terrain
is correct.
2. Is it worth fighting for this plot based on the given information, since there are several interested parties?
That depends on what you want to build. For a city villa, you need a different plot. A single-story house with a gable roof can also be nice and would be possible here.
therefore, we simply cannot imagine how a maximum eaves height of 3.5 m is allowed on the uphill side
I can. The city planners wanted single-story construction; the 5.70 m is also not enough for two story heights. On a slope, this is difficult to implement, so they allowed a basement, which could even be a full story. If they had allowed two stories from the start, on the valley side the impression of a three- or even four-story building could quickly have arisen, because the additional stories are not considered full stories according to the state building code. Additionally, they resorted to setting maximum eaves heights to definitely prevent this impression. This leads to asymmetrical roofs with too steep or too shallow slopes under the premise of maximizing living space. I suspect the city planners did not have this approach in mind at the time.
The given elevation difference also results in a slope from west to east
That is not relevant, since the ridge direction is given. It is about comparing the heights on the right side of the ridge with those on the left side. This determines valley side and uphill side. Clearly, on an almost flat plot, the result might not be clear. But that would then be a reason for exemptions due to atypical plot conditions.
Regarding the reference point, one should somehow calculate and use the center point of the terrain :/
Well. They themselves don’t understand what the predecessors intended back then. Perhaps the justification for the development plan reveals something. The statute itself certainly does not. It’s about the maximum value, i.e., the height difference most unfavorable to the builder.
3.5 m eaves height towards north
That’s how it looks according to the description. Only a surveyor can provide certainty – as so often.