I noticed in my Applications folder there is nothing listed as "Adobe" or "Flash Player".
I don't know if it will appear in Applications. Look in System Preferences. If you see a Flash Player preference pane, then it is installed.
I believe you can download and run Adobe's Flash Player uninstaller even if it's not installed. If you do that, you can be certain it is not installed: https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html
Would Apple install FP at the factory?
No.
Does Malwarebytes (updated Mac Version) look for these types of pop ups?
I don't use it so I don't know. If it isn't helping, I suggest you get rid of it. Be sure to follow its uninstallation instructions, as you would for anything you installed. Once it is uninstalled, please write back for additional suggestions.