iTunes seems to have it's own already defined (Control-Command-Z). Not sure how you can get rid of that. If you set your newly defined shortcut to that then it'll work everywhere...
No idea mate. iTunes is a bit of an odd one as it's a very old code base. I don't have a shortcut set for Zoom at all and I've still got a shortcut set in iTunes. Try setting your global shortcut to control-command-z instead of F5 as an experiment...