Hey huntz, thanks for the reply.
Problem 1: I probably should have looked a little bit harder for a plugins folder, lol. Found it. Uploaded Jetpack and activated. That's one problem solved (or worked around, I guess).
Problem 2: I currently have McKinley active. The same problem also appeared while using Crawford, so I doubt it's the theme. To make sure, I activated Twenty Fifteen and ran PageSpeed Insights again, but I've still got the same pop-ups.