Well the 7 enquires is just an average, sometimes it's less, occasionally more and very very really none.
Our employer calls it's being on call and not paid any extra for it, we are salaried if that makes any difference.
But do you have to continually monitor these e-mails?
Being on call would be (IMO) more like these e-mails coming in, most of them not urgent, but perhaps the odd one does need a reply and if so someone in the US office would phone you to get you out of bed to deal with that specific urgent one.
Being on call shouldn't mean you're actively monitoring some inbox, that should be someone actually doing that during working horse, rather you're available (as in at home, near a computer) so that someone can phone you if something urgent is required.
It isn't clear, from what you've said, how this is working exactly... are you literally staying up checking e-mails, or periodically checking them etc... you shouldn't really need to do that, you should simply be available to be called.
edit - ah FFS, this was some troll poster.
