Is there a way to open or close the VST Instrument editor or dthe Channel Editor? I don’t want to toggle visibility.
Is it possible to send the state (open/closed) using the Generic Remote control setup to an external controller?
No, on all counts except the command to open, but not to close the Instrument Editor.
The scope of the Generic Remote doesn’t include sending any data aside from what it sends out upon executing a command.
The commands listed in the Key Command dialog and Generic Remote commands are what’s available. there are no “Easter Eggs” or secret commands. (though there might be one or two G.R. commands that don’t work! 
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The term “Toggle Visibility” refers to the Track Visibility functionality only, not whether a window is visible, maybe keep that in mind when discussing programmatic topics.
Yes, kind of, it works fine here with a MIDI command via Remote, but as a toggle command rather than having separate open/close calls. First, load the VST or VSTi you wish to open/close. Then, bind a control to the command in your Generic Remote map: Command/Edit/Edit VST Instrument. It will ‘toggle’ open/closed upon repeating the same event. Note that plugins you bind in this fashion are based on the order you load plugins into your rack.
Yes, go to “Edit/Key Commands”. Again, this is a toggle rather than having separate open/close calls. Type Edit VST Instruments in the search, and build a key command. The catch here is that you must have a track selected first. Then your key command will be able to toggle whatever VSTi is attached to the track. If you want a specific track to be also be called up via key-command, then you’ll want to build a project editor that hunts for the track by name and selects it. Build a Macro that runs your logic editor, and then pulls up the “Edit VST Instrument” command.
P.S.
An alternative to “toggling” the UI of individual plugins in and out of view…
I often set up different working arrangements for different mixing or composing needs, save them to a workspace, and bind them to different foot pedals. A whole new workflow at a stomp. It works…
Take advantage of workspaces. You can easily set up any arrangement of windows/editors and swap between them using Key-Commands, and/or Remote Devices.
Maybe a workspace with all windows close might be a clear stating point for open/close counting. Then a little bookkeeping will help to remember the state of the window. Even if this is not nice, it might work this way.