First of all, please remember that PhD is not about learning; learning about many different areas/fields/subjects. More specifically, it is not about increasing you knowledge in breadth, i.e., you know Mathematics, you can now learn about physics, then you can learn about computer science and so on.
PhD is about training in research.
Ask your self this question:
How can I contribute to this area (may be theoretical physics or any) in this particular topic by utilizing the knowledge I already have (say, acquired during bachelors and masters) in this specific field (say, in pure mathematics)?
Once you get the answer to this question (it should be in the form of a nice research proposal) you will definitely be able to do your PhD in that area, which you would select and do homework for.
2nd part:
It really depends upon the institute and the department you are targeting to: what actually is the requirement there? And remember, some might not need GRE subject at all.
So, please make a list of the institutes/departments based upon your interests/priorities and mention their requirements. Then you would be in a better position to decide which one should you go for. Maybe, only because it is unavoidable or simply you can perform better in that.
I would suggest you to have a profound focus upon the first part. Chances are that you might end up targeting a Mathematics department only, still being able to contribute in physics. Even, otherwise would give you a clear vision of what should you do and what you don't.