My question:
How can I launch a new Activity in its own Task while using the following rules.
1) If the Activity already exists as a root of a another Tas
You can set the Activity's launch mode (android:launchMode) in the AndroidManifest so that it does not create new instances of itself if it is running, but will launch normally when it is not. Then you can start an Activity using Intent.
Activity
launch mode
AndroidManifest