The up arrow is the equivalent of a boost on Mastodon, adding to favorites is represented by a star. The down arrow is equivalent to the Dislike button on Lemmy and Friendica, Mastodon probably doesn't have an equivalent (Dislike will be federated this week). Compared to Lemmy, it works a little differently, as the up arrow there is the equivalent of a favorite.
The comment activity can be checked by expanding the "more" menu and selecting "activity"