Looks very possible.
Looks like.. should work, if "operand" accepts the name of your panel.
show_input_panel(name) returns a view, you can keep a reference to the view, and also keep track if the view is shown or not, There is also an on_change listener.
Probably with keybindings.
you can log inputs and commands to a console, See sublimetext.com/docs/3/api_reference.html
You need to hack hard and is complicated without testing, because some things that are supposed to work, in some very special conditions, does not work. So I can't tell with confidence.