Re: how many cortanas are there
Everyone has their own "Cortana App" so to speak. On Windows Phone it is integrated into the OS, but still an app. Cortana is being ported to Android and iOS as well, as apps.
However, the app is just an "interface" for the real Cortana, which resides in the cloud. Cortana is actually the "Personal Assistant" form of Bing, just as Google Now is the personal assistant form of Google search.
Whenever Cortana needs to recognize your speech, it is uploaded to the web, analyzed, interpreted, the answer calculated, then sent back to your phone.
So, is there one Cortana? Or many? Depends on how you look at it, I suppose. As an app, there are many. As the processing power behind the app, there is only one set of code that resides on many servers accessing data across the cloud to assist you with your issue.