Re 1 DOWN: I believe the answer is LION CUB : it is a beastly prince) (and LIB could stand for Party (political) Also ON CU is not quite "when expected "(on Cue), and is "crashing" in the middle!
Re 13 ACROSS: I think the answer starts with BAY (cry) but I've got BAY?E ?T? I was thinking this is the name of a concert hall or similar venue in the UK. I've tried all variations of the letters PITY about E (a note) to no avail!