To 1:
I can confirm that there's no button in BBEdit 15 to open or close the sidebar. But I never used a button for this action, the preferences in my BBEdit installations are set to automatically show the sidebar if more than one file is opened in the window. And I always use ⌘-0 to toggle the sidebar visibility, if necessary.
To 2:
In my BBEdit installation (BBEdit 15.1.3 & macOS Sequoia) everything seems to work a usual. If I drag a window icon from the sidebar of a first window to the sidebar of a second window, the the file hides from the sidebar of the first window, and if it's the last file in the first window, the the window closes automatically.
There must be something different with your installation, but I have no idea. – Maybe Rich Siegel has an idea.
Best wishes for the new year!
Ulrich