I don't know of any command for this, so I don't think you have missed one
How would VA know you are planning on making this an extern? Or just offer the option on any file scope variable in a cpp file? Since being a file scope, so "global" variable doesn't mean its an extern variable, not something we would want to try to do automatically.
Yes, something like that, it's very similar to "Quick actions and re-factoring->Create Declaration". It would be an added "->Create Extern Declaration", and generates that line in the header.