Is the dream of a home realistic with our financing?

We have already argued about that before. The median net income in DE is €3440 for 4 people. €2460 for 2 people. I don't know how many homeowners there are in the median. But I consider €4500 to be too high.

What kind of median? Which group/characteristic? All households and then the one "in the middle"? The median value is quite meaningless, in my opinion, depending on how the distribution looks.

Median German households - divided by number of persons in the household. Median is more meaningful than average in this case. Search for "Arm und Reich: Mittelschicht" and then the first result.

The diagrams in the link, especially the second one, are misleading, as one rather sees effects because the median was chosen. The real information is in the text, but some of the insights there are also due to the median. A statement would be provided by a diagram of the distribution, but that is not included.

The distribution of what? The upper diagram is a diagram that shows the income distribution of the population.

No, not at all, just look at the axes and their meanings. The left one is, ironically, %, the bottom one is the year, deviations from the media are color-coded in relatively broad ranges, you cannot back-calculate a distribution from that, especially because it refers to the median. The mean value is clearly below the median, but without a distribution, you cannot see which of the values makes sense here. The longer you look at diagrams, the more you realize that a lot of information is missing!

I actually find 3200 EUR solid for a family income, I would even go so far as to say that this represents the average! Typically, a regular earner + the second person with a mini-job/part-time job. Or am I actually wrong there?

That should be workable. If you have saved up good equity, are thrifty and determinedly pursue your goal, about 1,200 euros per month should remain for financing.