Floor plan house with granny flat - improvement suggestions?

In addition, I spoke to her about the topic of the utility room in the garage, that should also be possible, we would just need to send her a drawing from the architect.

Of course that is possible. But it involves the effort of insulating the walls. You can enclose a garage and insulate it just like a house, but you have to pay for the effort. In addition, as already mentioned, you need replacement rooms for the washing machine and so on, and that twice. The building authority does not care where your money goes.
And a parking space in the north, which I also favored with a different house design, must also be accessible to drive in and out. This means a limited turning radius on 3 meters wide.

Just on the building law side. Is it allowed for a utility room to be built within the 3m distance area like a garage?

Just regarding the building regulations side. Is a utility room allowed to be built within the 3m setback area like a garage?

Technical rooms are not living spaces, so yes.
In the OP’s case, the building authority is anyway quite lenient about a lot of things. They probably have to be, otherwise no one would manage with the plots.

I didn't understand you that way either. I think it is wrong to steer the architect onto a certain track right from the start instead of giving him time to possibly come up with another solution.

...I'm glad. Yes, you're right. It's not particularly clever to lead someone in a certain direction in advance. I only gave him a tip because he saw no other solution than to remove the stairs in the granny flat.

Before we now discuss each room individually like the brother’s room in the granny flat, the utility room outside, the living room in the granny flat, or your bedroom in the utility room, here is a quick draft with your exterior dimensions, your garden layout, and your entrance doors. Because these ideas were not so bad in principle, just because the staircase story was quite wrong (at least for seniors).
But caution: the wall measurements vary, in some cases only 10 cm... I haven’t adjusted much except the cupboards with 60 cm depth, 120 cm width, or 3 meters width.
Windows on the upper floor roughly correspond to those on the ground floor.
P.S. a straight staircase is nonsense with your problems.

Thank you very much for this quick draft. Here is my feedback:

Likes:
1. The living room in the granny flat is sufficiently large and reasonably well designed (the kitchen is in a small niche).
2. Granny flat has a small storage room for itself.
3. The hallway of the granny flat seems quite spacious.

4. The entrance of the main house - guest toilet, wardrobe
5. Parents’ bedroom with en-suite shower bathroom

Likes less:
1. The main house looks quite large, taking up a lot of space.
2. Where is the living room of the main apartment? On the 1st floor (chill area)? I find the chill area directly next to the parents’ bedroom somewhat unfavorable. It also looks quite small for a living room.
3. Does the staircase run from the hallway to the 1st floor? Will the stairs also be visible in the kitchen?

If the dimensions of the individual rooms were available, the draft could be better assessed.
I would also like to see a draft where the utility room is accommodated in the garage. Maybe someone is so kind and can help with this?

Technical rooms are not living spaces, so yes.
The building authority is quite lenient with the TE anyway. They probably have to be, because otherwise no one would manage with the properties.

I agree with that. In addition, the building parts that are built on the property boundary must remain below a certain height.

Where is the living room of the main apartment? On the 1st floor (chill area)? I find the chill area right next to the parents' bedroom somewhat unfavorable. It also looks quite small for a living room.

Why? That is your retreat area for the family. When teenagers meet, they can stay downstairs in the public area. Otherwise, you could also swap guest and bedroom…

Will the stairs also be visible in the kitchen?

As you wish. I created a storage room underneath.

The HT looks quite large, takes up a lot of space.

No, definitely not too big at about 8 sqm. Plus about 3 for the granny flat.