In the case of activating the auto- start manager, do I have to put the cursor on the programs as shown in the attached picture!!!!
Ticked/Checked/Enable is to allow the app to run on startup.
Unticked/Unchecked/Disable is to stop the app from running on startup.
At the moment, your screenshot shows the app is allowed to run on startup.
Hope that helps!
As @ronald1985 answered, a blue tick = app is allowed to auto-start.
I.e. from cold (not started by you) the app can wake itself up and do stuff. Like send notifications. (even after shutting them down / force closing).
By default, apps are allowed to Auto-start.
For apps you want notifications, leave the blue tick active.
For apps you dont care about for notifications, you can test having them off (no blue tick) , this could save standby power.