I have a question for my understanding, to which I have not yet found a clear answer.
Can data also be exchanged between the individual integrations?
For example, Homematic and Shelly are integrated in Home Assistant. Can I use the data from Shelly in Homematic?
It really depends on what you mean by “data”. You can create templates, scripts, services and such that would allow the data to be shared, but I’m not sure what else you are looking for beyond that.
Can you elaborate a bit more?
For example, I have a Shelly Wall Display with a thermostat and I want to use the measured values, such as temperature and humidity, as well as the set temperature in Homematic to control a heating actuator there.
So far, I read these values into Homematic via an http request.
Ahhhh, I see what you mean. Doesn’t homematic expose entities and services? You should be able to use a service to communicate information from your Shelly entities to your Homematic entities and vice-versa.
It sound like you are trying to feed a sensor value into the honematic ecosystem and then let that system react to the sensor value.
I am not sure that is possible as such.
What is possible is to let HA react to the sensor value and then use service calls to get the wanted action in honematic
You can certainly automate one device or entity based on the state of another device or entity.
If that’s what you mean.
Now I installed and played a little bit with HA.
I created automations and get now the homematic devices and entities writen. 
Thanks.