Is an air conditioner necessary in a south-facing location?

Yes, I'm completely with you on that. A cool house in summer is definitely great. I have already rebuilt our system twice (increase in the number of residents). Then maybe better to just finish it once and well.

The system should then be designed so that you don't have to think about when to open and close which door to have which temperature in which room.

Yes, then you need the three indoor units upstairs and at least one in the gallery and/or living room.

Free@Home planned. Although the air conditioning apparently cannot/does not have to be integrated there since it runs autonomously via room sensors, right?

Well, if you leave things out, a smart home becomes a pseudo-smart home with automations/remotely controllable devices. For control, you then always have to fall back on the system’s remote control... then that's rather not smart.

Air conditioners are like heaters. Your heater has (roughly estimated) 7-8 kW. With that, you create a temperature difference of 30-35 K from inside to outside. So why does the air conditioner require 11 kW for a difference of 10, at most 15 K? Just a thought.

PS: What kind of exclusive devices are those? Even the equity seems substantial to me...

Well, if you leave things out, a smart home becomes a pseudo smart home with automations/remotely controllable devices. To control it, you always have to fall back on the remote control of the system... that’s not really smart.

I just read again in the description of Busch&Jäger free@Home and it says that air conditioners can be integrated. I would have to clarify that in detail again.

Air conditioners are like heating systems. Your heating system has (roughly estimated) 7-8 kW. With that, you create a temperature difference of 30-35 K inside to outside. So why does the air conditioner get 11 kW for a difference of 10, maximum 15 K? Just a thought.

PS: What kind of exclusive devices are those? Even the equity seems quite substantial to me...

The devices for the "Material only" variant are from Remko (1x outdoor unit MVT 1403 DC, 3x indoor MXW 204 and 1x indoor MXW 524 plus small parts and connection cables). For the "Complete including installation" version, there is 1x Daikin 5 MXM90N outdoor unit, 2x Daikin R-32 wall unit Stylish FTXA25AW and 3x Daikin R-32 wall unit Stylish FTXA20AW.

I can't say anything about Remko (except maybe that I've heard it very rarely). Daikin is top. I believe the main cost driver in this setup is the fact that these are 4 to 5-way split systems. They are rather rare and therefore immediately quite a bit more expensive. If it is really going to be that extensive, it might be worth considering more than one outdoor unit. This usually shortens the line lengths and thus the installation effort, increases reliability, and lowers the equipment price. Of course, unfortunately at the expense of the exterior appearance...

PS: Just read today, 2020 will most likely again rank among the top 10 hottest years...

My parents have a semi-detached house as a 1.5-story building from 2001. I find it unbearably hot upstairs in the summer (like an oven). Although I can't really judge what has changed in terms of insulation in 20 years for a 1.5-story building where the bedrooms are upstairs, other than the insulation wool possibly becoming a few centimeters thicker. We ourselves have a cold roof with an insulated (24cm) concrete ceiling (20cm) above the bedrooms (full blast south side) and in summer, when the blinds are down from (9 o'clock), it's 25 degrees in the evening before going to bed. Which is just bearable. In your place, I would therefore install an air conditioner!

PS: Just read today, 2020 will most likely also fall back into the top 10 hottest years...

I certainly hope so, so that the purchase was worth it

In the "Complete including installation" version, there is 1x Daikin 5 MXM90N outdoor unit, 2x Daikin R-32 Stylish wall unit FTXA25AW and 3x Daikin R-32 Stylish wall unit FTXA20AW.

We also decided on the 10KW Daikin outdoor unit, but with 5x EMURA indoor units.
The installation effort and costs were also kept within limits since it was done entirely by ourselves.

P.S. The control via app also runs perfectly