See my apps, but the status is "installed" (LOS 17.1 with integrated fakestore)

[schdrag]

Can't install apps from the playstore. I succeed to login, see "my apps", but the status is wrong: I had installed these apps (on another android), so I should be able to install these apps again on the clean install.
I have the Pre-installed microG build variant with additional security patches from https://forum.xda-developers.com/t/rom-unofficial-10-0-signed-ota-lineage-os-17-1-for-xperia-z1-compact.4007983/
The google login is not stored at all, might be intended.
self check test of microg ist perfect!

[ildar]

I think you misunderstand this app. It is Fake store. If you need to install/uninstall something, use e.g. Aurora Store ( https://gitlab.com/AuroraOSS/AuroraStore/), you can download it from F-Droid.

[ale5000]

How already said Fake Store is just a dummy application, it doesn't do anything and cannot be executed.
It have to be installed because otherwise apps will nag about missing Google Play Services, but to install apps you have to use another store like Aurora Store or F-Droid.