I wonder about these items of functionality in the request:
3) Clicking on a different node when a tab is locked will open a toast message, saying "This tab is locked. Right-click on the tab to unlock it."
Would it not be simpler when I select a different node while in a locked tab, the newly selected node or new search simply opens in a new unlocked tab to the right of any existing tabs?
I can then go back to my locked tab at will? Any current selection in the locked tab should stay active.
Also, this would eliminate the need to grey out other nodes
5[?]) When a tab is locked, all other items in the media tree become:
5a) disabled (grayed out)
5b) not hoverable (this will require a tweak to the skins, I believe)