Sub question - if photons are light particles, moving at the speed of light, then do they actually experience time dilation themselves? i.e. from the frame of reference of the photon, is the local time for the photon ticking away in one frame, while the outside world appears to move much much faster? Or, relative to us is time on the photon moving very slowly?
The photon travels at the speed of light c. If you look at the expression for the time dilation, you will see that it tends to infinity as v approaches c. Remember that this relates the time experienced between two frames moving relative to each other at a constant velocity v. However the fact is that the expression fails when v=c, since you have a division by zero. This reflects the fact that it is impossible to do a Lorentz boost that relates two frames moving relative to each other at c. This in turn means concept of time dilation in an object moving at the speed of light, such as a photon, is meaningless. There is no such thing as the time experienced from the point of view of the photon.
I realise I probably wasn't very clear, but it's difficult to lay it all out in a small paragraph.
Another question this raises for me is that if photons move in a timeless state between 2 points, what accounts for the period of their oscillation in the particle/wave duality? If they are tracing the fastest path through spacetime, yet to them, the time dimension is non existent, how do they have wave characteristics?
We observe them since we observe time and they do have energy changes that we observe (I believe this is how colors and red shift work).
With regards to your second question, photons experience no time whatsoever. From the photon's perspective, they travel the universe from the point of emission to the point of absorption instantly.
If you want to understand this, I highly suggest watching this video explaining reference frames: https://www.youtube.com/watch?v=aRDOqiqBUQY
And this playlist of the excellent PBS Space Time series: https://www.youtube.com/watch?v=YycAzdtUIko&list=PLsPUh22kYm...
https://www.quora.com/Does-a-photon-experience-time
https://www.reddit.com/r/askscience/comments/2slx5n/how_is_i...
https://www.reddit.com/r/askscience/comments/2t8qr1/do_light...