Spontaneous Mission Control invocation
I would look at two things:

Check to see if Mission Control is listed in System Preferences -> Desktop &amp; Screen Saver -> Screen Saver -> Hot Corners

Check to see if Mission Control is listed in System Preferences -> Users &amp; Groups -> Login Items

Either of these might cause issues similar to at least some of what was described.

Additionally, when you shut down or log out, if the checkbox "Reopen windows when logging back in" is selected, all the programs that are running when you log out will be restarted the next time you log in - this might be re-launching some software that you don't actually want to use any more. I generally uncheck this box. If you select "Apple Menu" -> "Log Out" and make the checkbox unselected, you can then hit the "Cancel" button to not log out, and the checkbox deselection will be retained.