Your question is still unclear. Imagine that you had an unlimited budget, a very large laboratory, and a trained staff. What sort of experiments would you do to determine whether or not a photon "occupied space"?
The question is so vague and general in its current form that it's not really clear what you are interested in. I wouldn't know what sort of experiments you'd perform, nor what answers would convince you that the answer was that the photon did occupy space, or what answers would convince you otherwise.
Without this understanding of how you would reduce the question to experiment, I can't answer the question. Any answer would be highly misleading, esp. if you are using it to attempt to derive other results.
Science is supposed to be about questions that are ultimately testable. If you can't come up with a scenario that explicitly answers your questions through experiment, you are not doing science, but philosophy.
I suspect very much that the questions you have may be more related to quantum mechanics than relativity. But it's possible (because of the vagueness of the question) that I'm wrong. So I'll try and outline the relevant aspects relating to GR
1) GR is a classical theory, while photons are a quantum concept. We can certainly talk about whether or not light interacts via gravity though. The answer is basically yes. Light has energy and momentum. The "stress-energy" tensor that is the source of gravity in General relativity arises from energy and momentum, and how it is transported. Thus light contributes to gravity via its contributions to the stress-energy tensor.
That is about as much of an answer as you are going to get out of GR.
For a taste of the quantum questions (which should go in another forum, either philosophy or quantum mechanics) - suppose we have a light source that shines through two slits. We can experimentally see that it generates an interference pattern. We say that the light is due to waves, which interfere with each other. Suppose we make the light beam so weak that only one photon is ever in the apparatus at any given time. Does the light beam still generate an interference pattern.
The answer to this question is yes, and one philosophical interpretation of this result is that photons, regarded as particles, take multiple paths, and interfere with themselves.
Some people don't like this philosophical interpretation, which is in general fine, there are many. This particular philosophical interpretation is due to Feynman. People with different philosophies of QM often have a hard time communicating with each other, though if they both know what they are doing, they can both come up with the same answers to a well-posed experimental problem.
