Assessment of photovoltaic system, dimensioning

You’re better off with that question in the photovoltaics forum (google it).

A quick attempt: Distances from the edge depend on your wind load zone. Here with IIRC Zone 1 we only have about 10 cm.
For that system size, a kWp should cost around 1200 euros net. Your offer isn’t completely off, but it can probably be cheaper. Especially if, for example, the scaffolding from the house construction can be reused.
Which IBC modules are they? How many heat pumps? Are they black modules? SMA makes decent inverters.
At 45 degrees and a south orientation, you should regulate softly at 70%. That can be done much cheaper with equally good inverters from Fronius, because you can connect significantly cheaper meters.

Regards
Michael

Do we now have a total thinking(calculation) error or is the system way too small compared to the roof?

In addition to the good previous post: no, you are not on the wrong track. Go up to 10kWp or if more is possible, from >13kWp fully utilize. Arrange the modules on paper yourself on your roof and then order exactly like that.

I also don’t know why many solar installers don’t fully utilize the roof and want to sell more. It was no different for us and I’m glad for every additional module we now have.

I also don't know why many solar installers don't fully cover the roof and want to sell more. It was no different for us, and I'm glad for every additional module we now have.

It partly has to do with acceptable string lengths and the inverters.

If the system is larger than 9.9 kWp, a direct meter from the supplier is usually required. This means the meter cabinet needs an additional measuring field. From 30 kWp, current transformers are already used; with increasing effort, the costs also rise.

The standard modules are connected in series. A dormer casts a shadow. Shadows on series connection reduce overall performance. Ask the photovoltaic installer about the distribution and why they give this recommendation and calculation.
Anyone who just fills everything up with series-connected panels and promises full power despite shading has on paper the better kWp/€ ratio and delivers, in case of doubt, the worse functioning system.
Greed sometimes eats the brain, and that’s how these guys get their contracts.

If the system is larger than 9.9 kWp, a direct meter from the supplier is usually required.
This means the meter cabinet needs an additional measuring field.

In addition, you pay an energy surcharge on your production over 10kWp. Will rise massively in 2020.
Tip: Dimension generously according to your own consumption, use a hybrid inverter, and store excess energy reasonably in batteries and hot water storage.
If you don’t want to spoil the look of the house, use solar tiles. Although significantly more expensive, it also makes the house more valuable (so a good investment) – and with a low-voltage system on the roof and parallel connection, you also have no shading problems, no electrician on the roof, no fire load addition, and no high voltage above the living spaces. These are all disadvantages of standard photovoltaic panels, which nobody talks about and everyone accepts because no one questions them anymore.

, you have put an impressive amount of thought into your house. It should not go unmentioned that for many the motivation is, however, economic efficiency or, if you will, CO2 reduction. From that perspective, many of your recommendations are, in my opinion, counterproductive.

String lengths, shading: clearly that is important, but there are solutions for it without having to give up surface area.

The reference to another forum has already been made; I also received many helpful tips for our system there, which I then discussed with my solar installer and also implemented.