Lightroom Classic Was soll auf die externe Festplatte?? und was muss auf dem Rechner bleiben

Photos can be stored on any disk and in any folder you want (except for folders you do not have write permission to). It's entirely up to you. Keeping photos on an external drive is a solution that a lot of people use.

Translation to English: I import the images into the catalog in Lightroom. (now a question: can I remove the external hard drive from the computer?)

Not sure why you ask this. Explain further.

If you import photos on the external drive using ADD, or if you import from a camera card using COPY and select the external drive as the destination, the photos stay on the external drive, you do all your work on them while the photos remain on your external drive; and why would you want to remove it? Then LrC cannot access the photos. You could create Smart Previews as well, and then you could work on the photos without the external drive attached.

After you edit the images, there is no need to export, unless the photos are needed for some non-Lightroom use, such as printing, e-mail, upload to web site.

Translation to English: what can I still store/save on the external hard drive and what has to stay on the computer.

Only the software has to remain on the internal drive. The catalog file and previews should go on the internal drive as well, but if you need them on an external drive for some reason, like portability or lack of space on the internal drive, you can put them on the external drive. The photos, as I stated above, can be stored anywhere you want them to be.

The bottom line is that you have lots of flexibility here, to put things where you want them to be that would be best for your own work.