How do I see who visited, favourited and downloaded?

Each gallery's Activity tab lists its visitors, their favourites with the file names for Lightroom, and its downloads.

Open the gallery's Activity tab.
Visitors lists everyone who opened it, most recent first, by name or email (Anonymous when they left neither). The couple is marked couple.
Under a visitor, ♥ Favorites says how many photos they hearted. Copy file names for Lightroom copies those photos' file names, separated by commas.
Downloads lists the latest 50 downloads: who, how many photos, full size or 2048 px, and when.