ᐅ Extension and Vertical Addition to a 1965 Existing Building

Hello everyone,
my name is Christian, and I have been reading this forum for some time now. Since my plans are becoming more concrete, I am now making my first post.
I have the opportunity to take over my parents' house, and they would continue living there.
The house dates from 1965 but does not offer enough space for all of us, so I have the following ideas, always assuming that the renovation is approved. Of course, I will ask for permission before detailed planning, but for now, I need some help brainstorming.

The house currently has one and a half stories plus a basement. The basement ceiling is about 1 meter (3 feet 3 inches) higher than the garden, and the knee wall on the upper floor is about 1 meter (3 feet 3 inches) high, resulting in a noticeable roof slope.
The ground floor, which would serve as a separate apartment for my parents, currently has a kitchen, pantry, living room, dining room, and bathroom—unfortunately one room too few, so an extension here would be ideal.

If there is going to be an extension, ideally it would be two stories to create an additional room upstairs as a study or guest room. The extension would best be attached to one of the two gable ends (approximately 9 meters (30 feet) long). A timber extension would appeal to me.

However, to ultimately create the desired space for our family of four, an additional story would also be necessary. I am considering either a flat roof or a hipped roof so that another floor with a bathroom and three bedrooms can be added without much increase in height. Currently, there is an attic above the upper floor that is about 2.5 meters (8 feet 2 inches) high in the center, but in its current state, it would only provide space for a bedroom and bathroom at most.

Regardless of approval and structural considerations, I have the following questions:

1. Since the basement protrudes about 1 meter (3 feet 3 inches) above ground level, a quite high foundation would need to be built for the extension to align with the existing floor level. Would it make sense, for a bit more money, to also have a basement under the extension?

2. Does anyone have experience with how an additional story with a new roof might look in this case? Would the roof with the attic be removed down to the knee wall and rebuilt? That would mean removing all interior walls on the first floor as well?

3. Does anyone possibly have other suggestions on how to realize this?
An extension along the side wall would also be possible, but that would reduce the garden space in the area where it is most used.

For better understanding, I have attached a 3D sketch, although it is not yet fully to scale.

Thanks in advance for your advice,
Christian