The P2 popups were happening on my front end. It seemed to happen mostly while I was on my website doing hard refreshes on Firefox for my website (Cntrl+F5). As far as "difficulty loading my website" it only occurred after a cache dump and a hard refresh in Firefox, at which point my website would take forrrreverrrr to refresh (which was very unusual).
Then, oddly, when I was reporting the matter to my theme's designer on her forum (http://themeforum.elmastudio.de/), I got two more pop-up messages from P2 while on her website, not mine! Specifically, the pop-up notices were to inform me that I had received '1 new comment(s)'. I checked my website and indeed I had not received any new comments, nor had I ever received a comment notification in this manner (they come via eMail).
I wrote my theme designer, Ellen, a long message in her forum explaining the oddity. It wasn't until after I posted it --- I happened to notice what theme she was using for her WordPress.org forum -- P2!
At that point, I felt sure I was being transported through the Twilight Zone.
Possibly unrelated, but lately my website has been behaving very badly - fonts revert back to the theme's original design (http://themes.elmastudio.de/tatami/), and all of the revisions I wrote to in Jetpack's Edit CSS function sometimes is active and at others times they are not and the theme's original design appears instead. Oddly, the behavior and appearance is not consistent and it depends largely on where I navigated from to reach my website. For example, if I come my website via a link in a search result or from a link someone sends me about a specific article I receive in an eMail -- then none of my custom CSS design changes appear. What I see is the way the theme was originally designed. Yet, strangely, when I log into my website it looks OK (aside from the wonky changing fonts). It's probably unrelated, but at this point I think anything is possible.
I have my website behind a firewall at Sucuri along with a number of other security features I have activated that they offer, so I feel fairly confident that my website hasn't been hacked. But, I haven't contacted Sucuri about this matter yet (I was afraid they might think I'd lost my marbles). I wanted to get a reply from Automattic and my theme designer first.
Thanks! Hope you can help!