Oh yes, me too))) It's definitely one of my favourite movies now (if it may be considered a movie).
I don't really remember. I think it was aired on Boxing Day, but I don't know when it was shot. As far as I know EoT was shot way back in May. But yeah, the Doctor shows)) I laughed really hard when Hamlet talks back at someone (Polonius or the King, don't remember) exactly the same way the Doctor snapped at the Sycorax leader in The Christmas Invasion)))