What will the building authority say?

Google search for "distance terrace property boundary"

this has to be assessed "in terms of neighborhood law". Not "construction law"!

are multi-family houses permitted there? Is there a development plan?

Development plan see above

could there be something like an "imaginary" rear building limit line if you look at the neighboring properties like that?

No! However, from the street side

Where are the bicycles supposed to be stored?

Outbuilding (bicycle/tool shed)

Where in the residential unit is the washing machine supposed to be accommodated?

In the respective residential unit in the utility room

Saw it recently too. Terrace up to the border. Great when the neighboring house puts its shed on the border.

Honestly, I don't know if I like the relatively large utility rooms in the apartments. I know bathrooms with a niche for washer/dryer in many apartments the devices are spread out. Some storage space in the apartment is good. But what do max. 2 people want to do with such a large utility room? Your 2-room apartment is bigger than my 2 1/2-room apartment in Augsburg without added value. I know some who have 3 rooms under 70 sqm.

What does the building authority say? No idea. You have no knack for giving an interesting topic a headline.
Furthermore, you cannot see any measurements, numbers, or labels in screenshots. I can only guess everything because drafts are not foreign to me. But you cannot judge it like this.

this is to be assessed "under neighborhood law." Not "building law"!

Of course, it has to be seen under building law. Boundary distances must be observed. The house apparently breaks the rules with its height.
Besides, the balconies are much too close to the property boundary. The neighbor could certainly get a construction stop from the authority in such a case.

Development plan see above

Where? The development plan does not only consist of the legend; it is an entire document.
We had a thread here this week parallel to your strange single-family house about apartment buildings. Topic: drying laundry. The tenant has the right to a drying room for, among other things, bed linen. Has everything been checked regarding landlord obligations in Lower Saxony? Housing construction?

Regarding the draft, meaning the apartments themselves:
Where are the pipe shafts? Drain shafts? Correct your profession in your profile.
The apartments are habitable. They are okay if some mandatory measurements are correct. But you cannot read or assess that.
I do not find the attic floor successful.

I have to correct myself: The house construction is NOT FEASIBLE! Apparently, there is a building line in the front area that must be observed during construction. At least there is a building boundary in the middle that limits construction to the rear. Do the 3 dots mean garden land? And if you put 1 and 1 together, it will be a single-family house area, not one for multi-family houses. Just post the statutory text if you don’t want to read it yourself.

Proofs

Where are the cable ducts? Drainage shafts?