OK, I will try to remember the best as I can. As I recall, at one point using keyboard in Microsoft Outlook (my key reason for physical keyboard is that I do a lot of email), I did not get any suggestions for auto-completion or spelling - so I activate virtual keyboard. It was too big, and I turned it off. After this, the annoying keyboard problem started happening. It seems to me that it gets triggered with other keyboard settings, and if I use on-screen keyboard in another application.
To answer your questions specifically:
1) When keyboard is not working, the Logo-key does