Just to answer the question of whether you can speak before being spoken to when it comes to royals, I believe that you can't speak until you have at least been introduced.
Whenever I have seen footage of the Queen meeting and greeting people, the Queen approaches people, is introduced, the person curtseyes or bows, and the Queen says something along the lines of 'nice to meet you' and then the person meeting her speaks. I have never seen someone intiate a conversation with the Queen in public without being introduced first. I may be wrong, however, as I have never been in attendance to the Queen! I am just going on what I have seen. Whether that was the case 100 years ago in Tsarist Russia, I am not sure, but I would imagine that if that's the way the Queen still does it, nothing much would have changed.
As for clapping, I went up to London for the Jubilee and everyone started clapping and cheering when the Royal Family came out onto the balcony. They loved it, so I can't see why it would be deemed inappropriate. It's a sign of appreciation and support. Obviously in a church it may not be appropriate, but I don't see why it wouldn't be appropriate in a public display of affection for a monarch.
Rachel
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