Robert Karl Stonjek wrote:
The frequency of light is like a clock in itself - if the frequency is lower
then the clock at the source is slower as measured by an observer who also
measures that redshift.

As you indicate, this is pretty well known. One familiar application
is that high-redshift supernovae
take longer to fade than supernovae at low redshift. This rules out
tired-light models for redshift.
There's also an extra factor of (1+z) in the equation when you
calculate a distant object's luminosity.

I assume that this time dilation is taken into consideration when observing
pulsed transmission of the rotation of galaxies...

I don't know what you are referring to here. Galaxy rotation is
measured from Doppler shifts, not
from pulses.