There are some reports on the internet that confirmed the effect.
A study by Creaton says otherwise. Nowadays you can easily find confirmations for almost any theory.
There can be no problems with the tightness of the roof during installation and afterwards?
Yes, there can be – a Norwegian system from Sun-Net works without damaging the roof membrane.
How much does such a photovoltaic system cost? I know, probably a very general question.
Roughly calculate 1000€ - 1500€ for 1 kWh – also very general.
Can you get subsidies for that?
KFW supports with a loan for the system and a grant for the storage.
When does something like that pay off?
With proper sizing > 10 years (again very general)
Oh, and I read something about small business status starting at a certain photovoltaic size?
Small business status from 10 kWp – beyond this limit, you would also have to pay the energy levy. Questions that will help you further: How much electricity do I consume in which month? What is the typical load distribution over 24 hours? (you can measure this for a few days) How high is the "base load" in the house? --> Which consumers are always running with what power demand, e.g. refrigerator, air conditioning in summer?!? From this, you can then fairly well determine which system size makes sense, whether single-phase or three-phase, and with or without storage. You have enough roof area. The standard modules are high-voltage systems. I would not place something like that directly over rooms where I stay constantly. The sources on the internet all support these views – I therefore label this as opinion and not as a "scientifically" justified concern. And one more thing: The house will hardly be cooler with the modules on the roof. That was the goal, right?