I'm lost here, F.I.:
Also, I wonder why isn't there an "add shortcut" option in the RMB menu for this kind of toggable elements?...
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The mesh is the data part of the active object hence,
or perhaps since it is the edit object:
Sliding down the info area header at the top to reveal the messages gives you the context paths.
As for part ii) of your question adding an "add shortcut" menu, sounds like a good idea. This can be "hacked" by overriding say the edit translations operator in the menu.