As regards cancelling a "Mayday", in Europe it is (was?) possible to downgrade to a "Pan"
After losing an engine in a piston twin at fl200 immediately above the only remaining (CB limited) approach corridor to ORD on a seriously convective afternoon and realizing that there was no way I was going to be able to get a word in edge-wise to center that I would soon be on my way to a substantially lower altitude, I called Pan-pan, (not wanting to needlessly upset the applecart with a "Mayday"). My communication was, however, interpreted in exactly the same way as a "Mayday". An emergency was understood, and ATC made me enough of a hole that I and my passengers got out of the way, down in one piece, at an appropriate location, with a minimum of fuss, and nobody on the big iron missed his connection.
I asked about this issue in the (obligatory) post-emergency phone call with the FSDO, (they were happy with my actions) and I was informed that, in FAA parlance, there is no distinction betwixt the two.