Supernotes is well-designed to be used mouseless, but there are still some areas for enhancement. Onе of them: traversing cards hierarchy. I miss three shortcuts:
Maybe it is a good idea to assign keyboard shortcut to the Help (?) popup.
I came looking for exactly these shortcuts too.
In the case of ‘up’ and ‘down’ I think there’s some ambiguity.
‘Root/home’ is fairly clear — though whilst I go there currently, once saved searches / filter integration exists, I suspect that I’ll spend more time on some kind of saved search.
For ‘up’, perhaps a display like the Command Prompt could be used, to propose all of the parents as options to move up to if multiple exist.
For ‘down’, I’m not sure that I have any real request, since Find (Cmd+F) and Navigate In (Shift+Space) work well for me.
A shortcut for the cheatsheet would be nice. 
+1 to add a “go up” short cut. Multi-parent cards can bring up a quick selector, perhaps.
For posterity sake, “go home” and “go down a level” already exist!
Go home: CTRL+SHIFT+H (or CMD for macOS).
Go down a level: Select the child card with arrow keys or mouse, then press SHIFT+SPACE – this will open the card in the NoteBoard. Just pressing SPACE (without SHIFT) will open the card in the preview.
For go up a level, this makes a lot of sense. We still don’t have a hotkey for this, in part because as you mention @daniela1 it is not a trivial problem with multi-parent, but we will see what we can do.