You can certainly assign shortcuts for the leftmost icons in Engrave mode.
From within Preferences > Key Commands, you want:
Edit > Edit Graphically
Edit > Edit Frames
Edit > Edit Staff Spacing
Edit > Edit Note Spacing and
Edit > Edit Graphical Slices.
I can’t see menu items for inserting frames, but if you’re minded to go down the JSON-editing route you’d probably need to graft in something along the lines of
I hasten to add I’ve not tried these.
For your second question:
Actually, you can, but not in a meaningful way. (Try selecting a note in Graphical Editing mode, then switch to Frames Editing mode, then hit Cmd/Ctrl-Z - you’ll still be in Frames Editing mode - then hit Shift-S or Shift-F. See?)
In order to use Shift-S and Shift-F you need to be able to select musical content first, and when you switch between the different bits of Engrave mode you lose the selection. The Frames submode is designed for editing the Frames themselves, not their musical content, so it doesn’t allow you to select musical content. Without being able to select music, those shortcuts won’t do anything.