Can you check the package names of the apps? On F-droid website you can see it in the url, for example f-droid.org/packages/com.jens.automation2/ the code is com.jens.automation2. You should see the same name on the page of the app in settings if you scroll down.
If the names are the same than nothing nefarious should be happening behind the scenes.
Unknown source can mean it’s not from a built-in store. If you would be rooted and install the F-droid Privileged Extension it should show up there correctly. Maybe they just block reading this kind of info from F-droid.
On common Xiaomi phones the rom cooking community is very vivid usually, you can just replace the shitty default rom really easily. Start to look for roms and tutorials about rooting on xdaforums