This is more a philosophical question than a religious one.
Because while souls do appear in religion, they aren't concept founded by religion. Like you can believe people have souls but not believe in a God. Or alternatively, you could believe in a God but not believe that people have souls.
So its more the philosophical question in the "What happens after we die?" category than a religious "Is there a God?" type of question.
My belief is that not even humans have 'souls', or at least not in any way that I can understand, so I would say that Cortana does not have a soul. However, IF humans do indeed have souls, then why not Cortana?
The definition of a religion is the faith or worship of one or more gods or higher powers.
So yes, every religion is based on a God.
Let me take this opportunity to suggest that you have no idea what you're talking about and should probably stop.
You wasted your opportunity to say something wrong?
The definition of a religion, strictly the definition of the word itself, is as follows:
religion n 1. belief in, worship of, or obedience to a supernatural power or powers considered to be divine or to have control of human destiny 2. any formal or institutionalized expression of such belief the Christian religion 3. the attitude and feeling of one who believes in a transcendent controlling power or powers
Or if you prefer google's definition:
re·li·gion Noun: The belief in and worship of a superhuman controlling power, esp. a personal God or gods.
Which is what I said. By definition, a religion requires one or more gods or higher powers. Otherwise you're talking about faiths or beliefs, but not religion.