I think the issue you're facing is that the Character Viewer is no longer global, but is now per-app, so if you open it in, for instance, Safari, then switch to Finder, it will vanish.
Open it again in Finder & its stored size, position & last viewed will be different.
The advantage is you can keep it open in 2 different apps at the same time [with the one attached to any backgrounded app hidden] & be working on 2 different things.
The downside would be if that's not what you want to do ;-)
Simplest way to activate it is Cmd ⌘ Ctrl ⌃ Space but there's no 'close' command other than clicking the red dot, or temporarily, by switching to another app.