momo55 Can apps still run background tasks or after being closed in Graphene?
It depends on the complexities of the Android power manager, including which IPC intents an app registers for and which intents other apps issue.
if so, how can I actually completetly close/kill an app in graphene OS?
If an app is in a secondary profile and the profile is shut down with "End Session", those apps are stopped and the profile's storage encryption key is put at rest, so those apps really can't run (unless also installed in a different user profile that is active).
That said, hard-working apps may still corelate things like battery level and free storage space across profiles, so if a true separation between some apps and others is desirable then a separate device may be useful.