We want to show the widget on as many pages as possible, but the software doesn't have positions for widgets on every page. We're working on adding it on more pages, though.
There probably is an option to re-enable the down arrow, but I need to look for it.
The Wow, Sad, and Angry reactions don't count for reaction score points. They are considered by the system as neutral reactions. You can still see them under reactions received in your account, though.