Almost everything you said is correct. Photons do not have a reference frame, so time does not advance because for a photon there is no time coordinate system in the first place. It's not simply that photons don't experience time, it's that time and space don't exist for photons.
>They cannot change between emission and absorption, no matter the distance.
From the point of view of a photon, neither time or space exist. They have no reference frame at all. However, from an outside frame of reference that is travelling less than the speed of light, photons do change for example they get red shifted as they move through stronger gravitational fields.
Not to quibble about definitions of what "change" means, but I thought the red shift depended entirely on the relative speed of the emitting and receiving body? A laser beam for example could not be analyzed for its red shift, unless we knew the original frequency, because there would be no spectral absorption pattern to determine the shift. So we cannot tell how far laser light traveled before it reached our sensor.
Not a quibble at all. The redshift I'm referring to is the kind of redshift due to gravity, as opposed what you're describing which is redshift due to the Doppler effect.
I'm trying to come up with a scenario to understand the difference: Say I have a triangle of emitter, receiver, and a large body, all at a fixed distance. And the receiver would see emitted light both directly and bent around the body. The bent light would be red shifted?