Is a single-family house possible for 180k €?

We will have to provide additional funding of about 15k. Depending on the chosen model, we will have to pay between 50 and 400 € monthly (on top). So it is very difficult to compare.

Without additional construction costs, it should be possible. We paid 170,000 to Town & Country. 57,000 for the plot of land. Outdoor facilities are also completed except for the driveway (costing about another 2,000). Currently, there are 3,000 left from our 257,000 loan. So, the additional construction costs were about 27,000.

We paid 170 thousand to Town & Country.

But then you have a house in absolute standard. Or did a lot yourself. We didn't have many extras, just the essentials, and ended up at 220,000. For 129 m2.

No, unfortunately that is not possible, because from the 180,000 thousand, additional construction costs of 30-50 thousand still have to be deducted. The rest will hardly be enough, probably not even for a shell house plus finishing materials.
One calculates 1800 per sqm of living space + additional construction costs + garage + outdoor facilities + floor coverings and painting.

Well, without a basement, meaning less earthworks, 50k€ additional construction costs are already set very high, an acquaintance managed to get by with under 15k€ (without earthworks, which were included in the house contract, and without outdoor facilities, which are an extra for me anyway).
Otherwise, with that much EL, you cannot calculate 1800.-€ / sqm.
Nevertheless, 180,000 is of course extremely tight, if not actually too little.
An acquaintance had a prefab house built in Romania. The shell construction cost him about 60,000 €.
But you wanted to build solid anyway, I think?

Here is a breakdown of construction costs. That means: masonry, heating/plumbing, tiling, roofing, drywall – these are the really big items. Those who contribute their own work save money.

Here is a breakdown of construction costs. That means: masonry, heating/plumbing, tiling, roofing, drywall, these are the really big items. Whoever contributes their own labor saves money.

But these are only the labor costs, right?