Financing calculation for city villa with extensive outdoor facilities

First of all, thank you for your answers. A simple alarm system would also be important to me, since the house is located right at the edge of the forest and the property offers a lot of privacy but is also poorly visible. However, I might decide against it. The second bathroom in the children's area I want to keep minimalist anyway (sink, standard shower, and toilet). I myself had to share a bathroom with my parents and brother and still remember how annoying it was when four people wanted to leave at the same time in the morning.

Something like that can be implemented quite cheaply. It doesn't have to be a 5-10k€ system right away. Minimalist or not, it is another wet room, which accordingly costs. Children can; as already mentioned; also go downstairs if the guest toilet is slightly expanded.

A simple alarm system would also be important to me, since the house is located directly at the edge of the forest and the property offers a lot of privacy but is also poorly visible. [...] I am also considering, instead of a basement, possibly raising the knee wall on the upper floor a bit and thereby gaining an attic with a decent amount of space (with a tent roof the attic is very low all around).

The attractiveness for burglars can be influenced by whether Dacias or Porsches are parked in the carport ;-)
Knee wall with tent roof? – you would almost have to be allowed to print the money yourself for that. Then also as a substitution for a basement to save costs – how “practical” that would be on your property I already explained – but that would mean that the construction principle of a Pyrrhic victory would have been impressively exemplary understood ;-)

Are you just wanting to know if your calculation/budget fits but could actually afford more easily, only you don’t want to pay so much?
Or is this the absolute limit and it’s about managing with the 600k?

I suspect the latter here with good reason. Even the partial basement smells very much like an unsuitable attempt at cost control. My suspicion is that the OP developed a dream house shape ignoring the property, sent the plans to a general contractor with the request for an offer, only mentioned the basement in passing, and the general contractor then said: if a basement is to be included in this budget, then not in full size.

I see that the time has come to show the property along with elevations and the requested house design.

By the way, a dog is great as an alarm system. My avatar immediately notices when someone is at the apartment door and barks. At the house, he already guards the property. He can't protect it, but he notices everything right away and alerts. If I were a burglar, I would look for easier targets.

Just annoying that this alarm system usually goes on vacation too :p .

Yes, a dog like my avatar, but you can also keep a purely guard dog, especially with a larger property near the woods. It then lives outside only. Feeding can be handled by a neighbor or a paid service. But best to have several then.

I would like to install the air conditioning from the beginning, as long as the supply shaft to the upper floor is openly accessible.

So exactly zero lines from our air conditioning run through the supply shaft, so you should rather make sure to provide the necessary lines (cooling lines and control to the outdoor unit as well as condensate line either outside or to the nearest (!) drain). Large inclines are anything but desirable because they consume power and thus require the units to be sized larger.