Floor plan of a single-family house approx. 170 m² on a narrow 750 m² plot

Hi,
You have some conceptual errors that negatively affect the design. More on that shortly.
I find it likeable that you engage in the discussion here and also respond.
In advance:

- möglichst wenig Dachneigung im OG

How is two-story construction regulated in RP? According to your information, you have to build two stories, the house is declared as one-and-a-half-story, which, strictly speaking, does not exist. This needs to be checked, and then it depends on whether or how the knee wall exists, for example, the shower would have to be adjusted.
Budget: quite tight. What is meant by "planned DIY work: electrical, floors, heating, water"? Entire installation?

Das ist ein Weberhaus Balance 300.

Do you plan to build with Weberhaus? That is a prefabricated house... can you just install DIY work there? Or do you use it only as a template?
I am a bit puzzled that the Weberhaus Balance 300 looks completely different externally on their homepage than the presented floor plan on page 3. With your enlargement to 10 meters instead of 9.50, you are just over 190 sqm, planned is 170? … I found the city villa. I see no problem with a gable roof and a knee wall near 2 meters.

Regarding the design:
At first glance, I see some discrepancies regarding walls stacked on top of each other. For timber frame construction possibly not so relevant. I don’t know. There are also load-bearing beams.

The windows are placed quite arbitrarily: this will result in a different house that no longer has the thoughtful exterior elegance like the Weberhaus.

The windows themselves are too sparse for the room sizes.

Kamin: leichter Grundofen

The chimney is not drawn above (what is a light masonry stove?)

Regarding your conceptual knots:

a) Sun place

- Garage nicht vorm Haus, da damit Sonnenplatz verloren geht --> dafür Einfahrt nördlich neben Haus

Nur wenn die Garage vor das Haus kommt, haben wir weniger Sonne im Haus

If the garage is in front of the house, i.e., the western corner, the living area still receives enough sun during the day. The only thing that takes the sun away from you in the west is the pantry!
The plot will also offer you enough sunny spots. However, ask yourself whether a sun spot exactly where the garage could be predestined still warms your heart with a view of a mega expensive and long driveway to the north. I would probably prefer the view of the field without carport or garage.

Sun place: that brings to mind the terrace: if the plot is 18 meters wide and you want to drive past the northern side of the plot, then you need including stair landing a comfortable 4 meters. With hedge planting towards the neighbor (pray you can share that), it is 4.5 meters instead of 5 meters. Then you plan a 10! meters wide house (very big) and sit with your terrace practically on the neighbor’s lap… sorry, on the driveway. The question is, are you allowed to build the terrace on the boundary? Where I am, this is not permitted. And if it is permitted? Do you want that?
-> slender house on a slender plot.
-> Even in the shade there is light.
-> A pantry in the west does not take south sun.

b) Access "behind the house"

allerdings verbauen wir uns damit den Zugang hinter das Haus und nehmen uns viel Platz vor dem Haus, z.B. bei parallel gepflasteter Einfahrt.

As I said: you lose the beautiful view of the field.
The smart builder also uses a carport as wind protection and plans one meter more to go or drive through the carport.
Apart from that: planting 120 sqm costs 4 times as much as 30 sqm... the question is how long you need to shovel snow.
You have access, by the way, from the entire street side around the house.

Dann kommen wir wieder nicht hinter das Haus,

You always get behind the house!

Garage, Carport: Ja geplant, hinten auf Grundstück

c) Living room reduction

Möglichkeit später Wohnzimmer zu verkleinern und Schlafzimmer einzurichten (geplante Tür vor G-WC)

später die Möglichkeit durch eine Wand im heutigen WZ, ein weiteres Zimmer zu schaffen (Tür vor G-WC in WZ)

There is a difference whether you give an office or guest room a protrusion of 20/30 cm or give the living room a corner of about 3 sqm, which here reduces the living room corner by about 25% and practically makes it unusable as such.
If children are there, will the sofa then be moved?! Where to? Opposite the double door? Opposite the single door? Two doors next to each other?
You confine yourself completely with this niche solution; shifting is impossible because then there are doors...
The idea of the room partition also falls short. I assume for old age as a bedroom? Try to furnish the room with a double bed and wardrobe. You will encounter corners and narrow passages, which you also find in the shower toilet. This is not age-appropriate, rather you will stub your toes on the corners and edges at the bed, this corner, the corridor in front of the utility room, shower toilet, and this door, and in the shower toilet itself during age-appropriate walking.

There is no magic solution. Plan uncompromisingly for the next 30 years with a comfortable room and not with a room where you can hardly place anything without stubbing your calves. Even if you are not couch potatoes: one sometimes does not feel like anything, lies down on the sofa, the kids want to cuddle, etc. And before you have to move to the ground floor because of age, there are many years when the couch is more popular.

Regarding the floor plan:

Bestehen Probleme bei der Größe des Hauswirtschaftsraum, wenn Waschmaschine, Trockner, Technik und Lagerfläche untergebracht werden sollen?

No. You could even borrow 2-3 sqm from it for the shower WC. However, I would also reserve a small storage room upstairs; in a pinch, the office or a large closet will do for suitcases, decorations, etc.

Ist G-WC mit Dusche ausreichend groß?

Yes, barely. For old age, no.

- evtl. Küche zu klein

Not too small, but I just find it "incomplete". The tall cabinets lack connection to the U-shape.

- Cloakroom directly at the front door restricts freedom of movement when coming home.
- Pantry in the golden west
- Kitchen not a unit
- Living room is almost unusable, practically impossible to furnish.
- Two doors next to each other to the same room is poor planning (see above).
- Bathroom: T-layout disproportionately wide, can be done.
- Only the utility room door is well set (space for a closet behind it); office door can be moved.
- Walk-in closet consumes only space and wall. Closet in front of window - with 1.43 m width and a placed wardrobe, approximately 75 cm hallway remains -> one-way street without turning option.

Long story short: I would build a narrower house. Everything else is too tight for me.
Garage: Driveway left, then turn and drive into the transverse garage. That also provides privacy for the west-facing terrace. And yes, there will still be sun there.

Edit:
Pantry in the north, utility room to the front -> piping routes!

Wow, that largely makes the sample floor plan unsuitable. How much knee wall height are you allowed?

As icandoit wrote, that is still flexible. As long as you stay under 10 m in height and the specified roof pitch, it only has at most aesthetic limitations :)

I will answer in several stages.

how is the two-story regulation handled in the RP? According to your information, you have to build two stories, the house is declared as one-and-a-half stories, which, strictly speaking, does not exist. This needs to be checked, and then, depending on whether or how there is a knee wall, for example the shower would have to be adjusted.

We can build a maximum of two stories according to the development plan. The roof pitch inside the rooms does not mean a city villa, but rather that the knee wall is about 1.2-1.40m high. I know houses where there is almost no knee wall and the rooms become much smaller as a result. We want to avoid that.

Budget: quite tight. What is meant by the "planned own contribution: electrical, floors, heating, water"? Entire installation?

Because of my profession, I can carry out the electrical installation myself. The official acceptance will then be done quickly.
Tiles and laminate will be installed by myself and the family.
Heating means installation of the hydraulic part (pipes through the house, heating circuit distributor, floor insulation + stapling the underfloor heating under the screed, ...). Connection of the actual heat pump + buffer tank must be done by a specialist company.
Water means distribution of the water connections in the house, installing angle valves,... Connection of the main water supply is of course carried out by the water utility.

Are you planning to build with Weberhaus? That’s a prefabricated house... can you really do own work there without further ado? Or are you just using it as a template?
I am somewhat confused that the Weberhaus Balance 300 looks completely different externally on their homepage than the presented floor plan on page 3. With your enlargement to 10 meters instead of 9.50 you are just over 190sqm, planned is 170?... I found the city villa. I see no problem with a gable roof and a knee wall near 2 meters.

We only took the plan as a template. Unfortunately, the pictures and the floor plans do not match at many companies.
I roughly calculated the 170m² by subtracting 10-15% from the floor area because of the roof pitch.

Regarding the draft:
At first glance, I see some discrepancies concerning walls that are aligned on top of each other. Possibly not so relevant for timber framing. I don't know. There are also load-bearing beams.

The windows are placed quite arbitrarily: this will result in a different house, which will no longer present itself with the thoughtful external elegance like the Weberhaus.

The windows themselves are too sparse for the room sizes.

The chimney is not drawn in at the top (what is a light masonry heater?)

Ok, I have no idea about the statics. The architect/structural engineer (a firm) will surely hold us back on that. It might be that the timber framing method of Weberhaus does not have to pay much attention to that.
The issue with the windows is true. I think especially on the upper floor we need to improve that. But symmetry is not so easy.
Right, the chimney is missing on the upper floor. It should run along a wall in the hallway. A masonry heater stores the heat from fire and gases with its heat-retentive material and continuously releases it to the surroundings. These come in various designs. For a new house, a smaller model is sufficient.

Regarding your mental knots:

c) Living room reduction

There is a difference between giving an office or guest room a projection of 20/30 cm or giving the living room a corner of about 3 sqm, which here reduces the living room corner by about 25% and makes it almost unusable as such.
If there are children, will the sofa then be moved?! Where to? Opposite the double door? Opposite the single door? Two doors side by side?
You completely confine yourself with this niche solution; shifting is not an option because there will be doors...
The idea of room partitioning also falters. I assume this is for the bedroom in old age? Try furnishing the room with a double bed and wardrobe. You will encounter corners and narrow passages, which you also find again in the shower toilet. This is not age-appropriate; rather, you will stub your toes on the corners and edges of the bed, this corner, the hallway in front of the utility room, the shower toilet, this door, and in the shower toilet itself during age-appropriate movement.

There is no all-purpose solution. Plan uncompromisingly for the next 30 years with a feel-good room and not with a room where you can hardly place anything without stubbing your calves. Even if you are not couch potatoes: sometimes you don’t feel well, you lie down on the sofa, the kids want to cuddle, etc. And before you have to move to the ground floor because of age, there will be many years when the couch is more popular.

Unfortunately, I didn’t explain it enough. The door to the living room (opposite the utility room) should remain an option only by a lintel in the masonry. This door is not to be present at first, only if the room is partitioned into an age-appropriate room.
I will virtually try furnishing the optional room; it may be too tight.
I am also trying to find another possibility for furnishing the living room.

I have to think a bit about the other points.
I have attached another picture regarding the placement of the terrace.

We can build a maximum of 2 storeys according to the development plan. The roof pitch inside the rooms does not imply a town villa, but rather that the knee wall is between 1.2 and 1.40 m high. I know houses where there is hardly any knee wall at all, and the rooms become much smaller as a result. We want to avoid that.

You say building is permitted two-storey with a floor area ratio of 0.25 and a floor space index of 0.5 and with comfortable ridge height limitation. A "town villa" is not strictly prescribed here but is strongly recommended, even though I am otherwise quite glad that someone is finally thinking practically instead of excessively high knee walls. So, I would build a "town villa" here – with a gable roof at 25°. 1. The floor area ratio argues against area-consuming storage space, such as a cellar or attic. 2. The ratio of floor space index to floor area ratio of 2:1 strongly suggests designing the upper floor as a full storey. 3. With a "knee wall" (here practically: roof pitch lowered down into the upper floor), the roof (as a rafter roof, a truss roof is then not possible) becomes more expensive; the attic pays for itself somewhat in this regard. Incidentally, I would also take a look next door at Fingerhut to see what they could offer you.

Symmetry is not quite that simple.

That doesn’t matter at all: symmetry has zero moral value and may absolutely be mercilessly dismissed.

The door into the living room (opposite the utility room) should only be an option through a lintel in the masonry. This door should initially not be there, only if the room is later separated into an age-appropriate room.

At "currently 32" you will build once or twice more before you can speak of "age."