Re The Queen.
Legally she does/would have to bow to the President of the EU, as she would be/is only one of his subjects, whereas when she meets say Obummer, they meet as equals, as Heads of State.
Apart from that she is very pro the Commonwealth and when we leave that will come into play far more. She is also nobody’s fool and can see just what a useless bunch the EU is.
However for her to come out twice, effectively saying vote Brexit, shows how concerned she is we make the right choice.