Can I add my own activity types or change the emojis?
Yes. Settings, Operations, Activity tiles lets you add tiles with your own name and emoji, reorder them, and hide built-in tiles you never use.
Yes. Go to Settings → Operations → Activity tiles on the web dashboard and click Add a tile. Give it a name (up to 40 characters, for example Music and Movement) and pick an emoji, either from the row shown or by typing any emoji from your keyboard. The tile appears in the logger next to the built-in ones, on the web, in the app, and on the room tablet, and parents see its emoji and name in the feed.
From the same card you can rename a tile, change its emoji, reorder tiles with the arrows, and remove one. Removing a tile that already has entries keeps those entries' emoji and parks the tile under Removed tiles, where you can restore it.
If there are built-in tiles your program never logs (Tummy Time, the therapy tiles, and so on), click Choose next to Built-in tiles and click the ones to hide. Hiding only removes them from the pickers; anything already logged still shows.
One thing you cannot do yet is rename a built-in tile or give it a different emoji. The workaround is to hide the built-in tile and add your own with the name and emoji you want.
Related: Add your own activity tiles.