Location of the house, parking space & driveway on the property?

Unfortunately, your municipality does not provide the development plan and the written regulations online, so some questions remain unanswered. However, the city has apparently already initiated the first amendment of the development plan. Find out whether your property is affected. You can casually present your drafts and ask for a rough assessment of the likelihood of approval. Depending on the status of the procedure, submissions are still possible that could be taken into account in the amendment.

In den rot schraffierten Flächen dürfen Stellplätze gebaut werden.

So parking spaces are excluded outside the red-bordered areas? Does this also apply to garages?

Dein Nachbar, der in 4, muss die andere Firstrichtung wählen.

Are these building proposals, or is the ridge direction actually supposed to be fixed by the representation?

schon der Platz für sie wurde gewählt, ist aber wohl nicht bindend.

The legend is missing, so we can only speculate.

Sind Bauvorschriften grundsätzlich einzuhalten

Yes. But there is the possibility of deviation (from the state building code) or exemption (from the provisions of the development plan). In both cases, an application (form) must be submitted and well justified. Both are subject to fees. Of course, you can also take legal action against the development plan (norm control procedure). However, you can then take your time with your building plans, meaning: practically hopeless!

So outside the red-bordered areas, parking spaces are excluded? Does this also apply to garages?

If I understand the development plan correctly, this applies to all kinds of parking spaces including garages.

Are these building proposals or is the ridge direction actually supposed to be fixed by the representation?

According to my understanding, these are only proposals. The ridge direction is not fixedly specified.

The legend is missing, so we can only speculate.

I have attached the complete development plan including legend and description to this post.

Yes. But there is the possibility of deviation (from the state building code) or exemption (from the stipulations of the development plan).

We will inquire with the city next week whether and how deviations from the development plan are possible.

If I understand the development plan correctly, this applies to parking spaces of all kinds including garages.

It is a pity that development plans often fail to clearly formulate urban planning intentions. This can already be seen from the numbering here: Why does the numbering start with 2. and why are the subpoints of 2.5. Parking spaces and garages numbered from 1.1 to 1.5, and why are there conditions related to parking spaces and garages again under 3.4.1. Wall height that have nothing to do with the wall height?
IMHO, you could also place the parking spaces outside the red line next to the house, like in variant 2 (parking spaces instead of garage). Maybe the garage in the basement or in the northwest corner of the garage zone.

The ridge direction is not fixed.

I agree.

is probably not binding.

Probably not for the trees on the properties, but the location of the street trees seems to be fixed.