Prefabricated house including land planned - financing

... per connection!

But again for understanding... it says in the price included: including plot, including incidental building costs, including outdoor facilities... so practically everything that in my opinion belongs to it and at the end of the list: fixed price guarantee.

Every provider who mentions something about fixed price will then put an asterisk behind it and link it to the construction description. For example, it says 5 sockets in the bedroom, that is part of the fixed price. If you want more, you have to pay extra. So far so obvious and more or less expected by the builder. It gets more difficult with things you cannot assess: load-bearing capacity of the soil at least X kN/sqm, no water-carrying layers, soil suitable for backfilling. Some providers also calculate with the lowest level for snow load, wind and – important here in the south – earthquake zone. The fixed price includes exactly what is stated in the construction description. If it says "earthworks up to 30 cm" you pay for everything that goes deeper. It is important that all things that are also listed in the ad are described as precisely as possible.
Outdoor facilities for example can mean a lot. How much paving is included, up to what price per square meter, are you even allowed to choose the pavement or does the construction company decide, what about fence or hedge, is turf laid or seeded, etc. All of these points can change the price and tendentially the construction company will always opt for the cheaper option.
If I were you, I wouldn’t transfer any money before a contract is signed and part of the contract is the construction description. Otherwise, you buy a pig in a poke and keep throwing money after it.

Just out of interest: what costs (order of magnitude) can be expected for electricity and water connection?

You can easily look that up on the website of the respective suppliers. EnBW for example calculates as follows (if they are even responsible there)

Whether 10m of connection are sufficient again depends on the plot. For this, you also need a multi-service entry which again costs money.

Thank you for your answers. Next time I will know significantly more. I will also have a lawyer review the construction contract. I think that is well-invested money. It has nothing to do with distrust, rather with security.

Protection is good, but the lawyer usually cannot read a construction specification. It is worth investing a few evenings for that; there are good books on understanding construction specifications. I have some from Stiftung Warentest and the consumer centers. They also include the usual points where construction companies save money. Additionally, the construction specification can be checked by an expert before signing the contract. However, this is rather unfavorable during the selection phase; if you have 5 providers checked, it gets expensive.