Order of Navigation sections in admin. Changeable?

Also, it would be nice if closed full-width nav widgets would display on a hover, the same as when they’re ‘minimized’. It would save a click and feel faster. (Would be nice if widgets, generally, could display/open on a hover, like when dragging a widget to a closed sidebar. Or am I missing something?)

No, you aren’t missing anything. You could alter the functionality by editing the core code, but that is not recommended for obvious reasons. Instead, you might want to try making your own admin theme:

https://codex.www.ads-software.com/Creating_Admin_Themes

Thank you.

You’re welcome!