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If Ctrl-3 is identical to ESC, I should expect vim quit insert mode to normal mode when Ctrl-3 is pressed, like ESC usuallly does, however, actually, 3 is input, so Ctrl-3 shouldn't be the same as ESC or Ctrl-[, should it?
@statox yes you are right, neither it deletes a line (map to dd), nor echoes 'hi' (map to echom<Space>'hi'<CR>), however <C-P> works, so I think the problem is related to <C-S> only, not mapping