Buying a house without a mortgage loan

I am not suffering from a fear of missing out and I am definitely not naive. My children are actually partially grown up and we have managed quite well here without a car. If I were naive, I wouldn't have asked here. I wouldn't read and could sleep wonderfully at night. But since I am thoughtful, read a lot, seek advice and even hire an expert, I would honestly say I am not approaching the matter with naive eyes. And if I were, I would pay off 1% or something like that.

A few factual points, because in my opinion there is a lot of unnecessary aggressiveness here, but the OP is rightly seeking help.

a) The area (Palatinate Forest) is one of the poorest regions in Germany (Pirmasens district not far away is the bottom in West Germany). Accordingly, land prices are low and house prices are also dirt cheap. This obviously does not apply to new builds (what a surprise), but the purchase price is therefore not suspiciously low.
b) A quick look at the train app shows that the town is connected to Mannheim every half hour by S-Bahn (travel time about 50 minutes). However, this is not really a contradiction to a). Because the S-Bahn connection might be a criterion in the south of Munich, but not in the Palatinate Forest. People simply don’t want to go there. There is simply nothing there. Life only begins below Neustadt or Landau. The Palatinate Forest is deserted and breathes a morbid charm. That is why I agree with the bank, which considers the purchase price (albeit for another house) more as too high than too low. A plot of land there with an existing building on a railway line, which a homebuilder would first have to tear down, has rather a positive than a negative value. If you move to such a dump, it is usually to build a new little house in a nice location with an SUV. Therefore, the mentioned property should not meet with widespread approval.
c) The OP has no car and works at a train station (in Mannheim?) and would probably still be able to get to work reasonably. If not: caution. Buying a house that leads to a job loss is harakiri. But what about the husband? Does he also continue to get to work (even if only part-time)? For this, 50 minutes one way is probably too much. Are there possibly jobs in the region (Neustadt?) reachable by train that are worthwhile even for part-time?
d) Please make clear to yourselves that he lives in the middle of nowhere and while the S-Bahn regularly gets you to work, social life is certainly noticeably more difficult. On the other hand, maybe that is exactly what you want if the city no longer feels safe to you?
e) Please do not underestimate the renovation. Do you have experience with that? How do you want to manage that without a car and driver’s license? Here I see the big snag. Unless by chance the electrical system and water pipes were done in the last 30 years, this can become a bottomless pit. It is then no longer a matter of tens of thousands, but quickly hundreds of thousands of euros (the facade will also have to be done sooner or later). With your wealth/income you can hardly rely on external craftsmen. So I fear that even if you agree with a-d), you will have to renegotiate the price again. Also inform yourselves again about subsidized loans. You have 3 children, so there should be a cheap loan (in the 1% range) at a promotional bank (e.g. the L-Bank in BaWü, I don’t know about R-P). They also make sure that you only get this if you have the creditworthiness for it. I understand that for floors, wallpaper etc. the cheapest is enough for you. But if the pipe leaks, that no longer works. If the heating has to be replaced by a heat pump and the house doesn’t get warm anymore because the facade is not insulated, likewise. These are points where unfortunately you cannot save.

I can already sense once again the lack of ability among high earners to imagine a less comfortable life. ;) Of course, it's less convenient without a car. But please don't forget that we're talking about Weidenthal here (I can say that openly since the OP shared the ad with us). This is not a village of 400 inhabitants. The train station is located directly on the route between Kaiserslautern and Mannheim/Ludwigshafen. I used to commute there as a vocational school student, so I still remember the stop. I believe a train runs every half hour to hour in each direction. You can manage with that, as long as the trains aren't striking. But strikes usually affect long-distance trains rather than commuter trains.

I would never risk my job by moving. If I can't get from home to the job, then I simply can't move there, it's that simple. And vice versa, basically the same. I would never apply as a saleswoman in Bad Dürkheim because I simply wouldn't be able to work the shift hours. If I had a car, I would even move to Elmstein or Esthal, where some buildings have been completely renovated for 250k. But since I wouldn't be able to continue my job then, I can't buy there either. As I said, if I were naive, naive or the like, I would simply buy!

The question here was how a house purchase could be financed, and the OP shared the real estate listing with us for a better assessment of what we are talking about. Now exactly this is backfiring on her. First, the price was criticized without knowing the region, now it is the accessibility and the lack of a driver's license. A 50-minute commute to work is considered practically impossible. I had that in the big city with a 25 km distance by car as well, at least. By public transport with transfers it was even longer. Maybe we should get back to the topic and not try to talk someone out of their lifestyle.
feel free to report what the appraiser says.

And of course, I see problems especially in material procurement. I am fully aware of all this. I haven't been doing this only since yesterday. I have someone for electrical work, and also for plumbing. But of course, like everything in life, that is not guaranteed either. Since they are friends/relatives/acquaintances, it could also happen that they leave me hanging. But you simply don't know that from the beginning.

Actually, I could also move to the Pirmasens/Trippstadt region. But down there, it is really very dead. Here in my town, it is only so expensive because there are massively many teachers or BASF employees, since it is practically right next door. And then also BW.