Just before signing a contract with a construction company, what should be considered?

Have you already sorted out the financing at all?

And just out of interest: is this the very first plot/house? Or have you already looked around, compared different providers, thought about some technical things (e.g. what kind of wall structure is there, do I even like it...)?

We clarified the financing at the beginning. This is really the very first plot/house. We have not approached any other BF either. We are told that the situation with plots in the city of Leipzig is such that we could wait years for the next opportunity. And finding a plot on our own or with a realtor actually looks very, very difficult; we have been searching for about 6 months and have found nothing so far. That means one would either have to leave the city, which we do not want, or turn to a BF.

Of course, it has also become a seller's market.

We are building just "around the corner" and searched for a plot of land for significantly longer than 6 months, ultimately paying >300k. It is not only difficult... it is almost impossible to get a plot here currently :)

Which region of Leipzig is it? North? South?

Room height on the ground floor of 2.60 m should not refer to the shell construction - otherwise it will only be effectively 2.40 m later with screed...

Otherwise, have the VT + construction service description checked.
If necessary, the Verbraucherzentrale will do this on site.

Lindental, for 190€ per m2, 900m to the S-Bahn (Wahren), very quiet street. How big is your plot and where? That sounds like Markkleeberg :) Ours is just over 1000m2. No idea how bad it really is with the airplanes there, we were there 4 times at different times of the day, it was very quiet.