Technically no, photons don't always have a speed of 1C, as C is the speed of light _in a vacuum_. In more dense matter the speed of light will slow down.
Technically true and also completely irrelevant for this thread.
"If the emitter is coming towards us that would blue-shift photons," is, I think, the point of the previous person's comment.
Blueshift == relative speed difference, which manifests for a photon in the form of more energy in the form of a shorter wavelength no? Gamma rays being an extreme example.
That much blueshift means that much more relative speed towards us.
Redshift being the corresponding speed difference ‘away’.