Hello @Notlaw, thank you.

The first demand is made impossible by FF for Web extensions, the Boomark History window is not customizable and no add-on can run within it, sorry.

The second one you mention is in fact hitting a bug I opened on FF some time ago https://bugzilla.mozilla.org/show_bug.cgi?id=1531539
=> we are waiting for it to be corrected by FF so that it can work.
=> Meanwhile, the work around is to drag the folder you want to move to the bookmark bar, and to drop it into the "Bookmarks Toolbar" folder inside of BSP2, at top of the bookmark tree .. and the result will be the same.

Thank you, aaFn.