Not sure what you’re asking here. This is not a screenshot from my plugin.
I see. You’re saying that it isn’t showing tags as a menu in the sidebar view? As far as I remember, it should work only in the main area. I’ll take a look to either remove from sidebar or add the menu.
No. There are 3 places where a widget can be placed: top of page, bottom of page and sidebar. That’s a framework thing.
If you have Pages, then you can create a custom block and place it anywhere, AFAIK.