I have removed some apps via right click on the tile and by clicking on "delete", but I still get update notifications for some of those apps.
Some files are still there. How to remove an app completely?
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Are you sure you've removed the app or just the tile? To remove the app, right click it's tile and choose Uninstall. Then it should ask you for confirmation, click uninstall again and it should go away.
Otherwise there is a risk that you just removed the tile from the start screen and it's still available under All programs. You can get to the all programs screen by right clicking an empty area of the start screen and press the button that appears on the bottom right.
You can use DISM or Powershell to remove the apps:
DISM.exe /Online /Remove-ProvisionedAppxPackage /PackageName:PACKAGENAME