(Personally, I agree with the idea that time is an aspect of change, and not the other way around. But the physics does not presume that, and still allows for a consistent interpretations.)
None of the above. You can anthropomorphize the happy photon, but you have to bring the rest of relativity along with you. And relativity presents an interpretation in which time does stop for the photon, causation is temporal, and events are predictable.
Even if we imagine a the photon has a sense of time of its own, there is still no spatial movement seen by the photon relative to our perceived space.
Taking the same limit that reduces the passage of time to zero, also affects space. The photon sees our length completely compressed to zero in whatever direction it is travelling relative to us.
We are always completely in its peripheral vision, whenever it might rotate to look at us, we disappear. (We are like Carlos Casteneda's death, always straight left of its line of sight, even when it turns its gaze.) Whatever direction it might choose to move in our space, the space won't let it. In effect, then, our whole space is reduced to a single point. And for it to bounce around our point-sized universe does not ever require, or even allow for, motion with velocity.
To the extent it might perceive the remaining dimensions of our space perpendicular to the one in which it is traveling, there is still no real causal sense. Things in our universe might cause it to turn, relative to us, but the photon sees this as other things moving around it, and not as causal effects upon it.
Further, those things moving around it are stuck where they are relative to one another, and in some ways relative to it. They cannot get closer or farther, or change their other effects upon it in any way. From the photon's point of view, our time is frozen, because when the photon's time passage relative to us became zero, so did our time passage relative to it. That is what is relative about relativity. And the bizarre view available to it of our frozen time would have to be one in which everything we see as successive, is actually happening at once.
This does not mean, necessarily, that the photon does not experience causation, but that the causation is independent of anything we might perceive. It gets its own frame of reference, in which it can be affected by gravity, etc., in ways we would not perceive, just as it sees no effects on or from us, because our timelines are independent. It sees as static what we see as changing, and vice versus, with each of us having a complete map of the other's timeline embedded in its view of space.
Rudy Rucker imagines extra spatial dimensions in which we might be extended and participate, but never perceive. Our space would be like that to the photon. Except that additionally, since our timelines are perpendicular, all side-effects of its participation in our space are frozen, still pending but already done, so there will never be real evidence to the photon that we exist or at least that what happens/ed here ever affects/ed it in any way.
Another way of looking at this is proposed by Wheeler and Dyson. The slickest way to formulate the change of frames of reference is as four-dimensional rotation in a hyperbolic space. As we speed up, time rotates (rotatesh ?) relative to space. Attaining the speed of light relative to us, then, is a (hyperbolically) perpendicular rotation, which takes its time dimension into (a bizarre reshaping of) one of our spatial dimensions. This indicates all the same effects but is far harder to interpret anthropomorphically.
