Not really. It uses the same shell, but the text editor part is completely different (and from what I've heard, much faster, especially on large files).
What? Not even close. That's a ridiculous statement.
They both use electron, but Microsoft is baaarely using it for some UI pieces. That's really the only similarity between them.
Not really actually. It uses the same shell called Electron as the native host. But other than that, completely different implementation.