Hi guys,
But if there is no such thing as a permanent self or soul, then the obvious question is - who is this person that eats, drinks, breathes, thinks, forms relationships and has a career?
In reported speech, trying to keep as much of your wording as possible, I would say
But if there is no such thing as a permanent self or soul, then the obvious question is who this person is that eats, drinks, breathes, thinks, forms relationships and has a career.
No question mark is needed, because the reported sentence itself is not a question.
Best wishes, Clive