The phrase the King is dead long live the King exists to make sense of the whole concept.

A throne is never empty. The second Elizabeth died, Charles became king.

This threw me back to studying Ionesco at school - "Le roi se meurt! Vive le roi!"

But coronation will not occur for about a year.

Coronation is just a ceremony.

Yes I think this is the case. The death announcement from Buckingham Palace refers to him as such.

"The Queen died peacefully at Balmoral this afternoon.

The King and The Queen Consort will remain at Balmoral this evening and will return to London tomorrow."