Expanding Universe : Cosmological redshift?

Doesn't look like there is much other evidence, apparently galaxies are moving apart, although there doesn't seem to be any actual visual images seen of galaxies moving apart, assuming they appear to move slowly at great distances, so maybe it would take a lifetime to see them move apart, only redshift is evidence, if you interpret redder galaxies as galaxies moving away from us due to dopplar shift, but not all galaxies are moving away from us, some are moving towards us? which doesn't make sense? with an expanding Universe theory? They should all be moving apart?

However the further away galaxies get, the redder they get? so there is some sort of correlation with redness and distance, suggesting redshift theory is somewhat valid, but galaxies matter in the distant past may have been redder? because it was hotter, with larger more expanded atom's creating a red shift effect,

No, the only evidence directly for expansion is redshift. Now, there is other evidence which suggests that the Universe was smaller in the past, such as the homogeneity of the cosmic microwave background. Of course this doesn't show the expansion is accelerating --- that comes exclusively from the redshift of distant supernovae (and the finders of such were recently awarded the Nobel Prize).

Well, the expansion is one thing, the increasing rate (or acceleration) is another. The former is so well established by thousands of astronomical observations of various types (essentially all of modern astronomy) that to figure out how it could possibly wrong is very hard indeed. The acceleration is a fairly recent result and has only about 5 sigma statistical significance in the data. It could be wrong without wrecking very much in modern cosmological theory --- in fact, explaining the acceleration theoretically has not really been done. Saying it's "Dark Energy" just gives a name to the problem, it doesn't explain it. Nevertheless, you can't just dismiss a 5 sigma result.

There are certain types of nova's that will always emit their light at the same intensity. Since intensity of light falls of with the square of the distance from the source, these nova's can be used to calculate the nova's distance from earth, even when these nova's are in distant galaxies. The nova's also emit their light at the same frequency which makes assessment of their redshift very accurate as a measure of velocity. When you plot the redshifts as a function of distance for these novas, the curve indicates that not only is the universe expanding, but 7 billion years ago the rate of expansion increased.

These measurements are very accurate. Unless there is some unknown physical phenomena that is giving us the illusion of an expanding universe, the redshift/distance evidence is compelling.

Cosmological redshift is good enough.

Older galaxies are further away.

You might answer your own question if you read my theory, given below, it should help.