The parallax angle of such distant objects is way too small to be measured. In general, the farther away an object, the smaller is its parallax angle.
I think it's currently impossible to do that - specifically, to measure the distances of ALL the galaxies. There are just too many Astronomers might take a small section of the sky - say, a square degree or even a fraction thereof, analyze the galaxies in such a section, and extrapolate. As to the measurement itself, there are different methods; the Wikipedia article on "cosmic distance ladder" can give you a general idea. In summary, the farthest galaxies are simply measured by their redshift. That is to say, the farther they are, the faster they move away from us; and this can be measured using the Doppler effect.
The parallax effect becomes unnoticeable after 1,000 light years.
The evidence for Hubble's Law, which shows the relationship between distance and recession velocity of galaxies, was collected through observing the redshift of light from galaxies. Astronomers used spectroscopy to measure the redshift of galaxies, which is caused by the Doppler effect as the galaxies move away from us. By studying the redshift of galaxies at different distances, astronomers were able to support the idea that the universe is expanding.
Parallax is defined as an effect in which the direction of an object differs when viewed from other positions. A sample sentence is shifting perspective creates a false parallax.
all galaxies are constantly moving away from each other and are increasing in speed due to the lessening effect of gravity over the distances between galaxies and the theoretical dark energy which scientists have yet to prove the existance of
Parallax helps because the bigger the parallax is the closer the star is. Knowing the distance helps to determine the "absolute magnitude" of a star, not just how bright it appears.
The Doppler effect changes the position of well-known lines.
Have no real effect on the merging "colliding" galaxies
They don't
The definition for the word parallax is "the effect whereby the position or direction of an object appears to differ when viewed from different positions, e.g., through the viewfinder and the lens of a camera."
shifted to longer wavelengths, indicating that the galaxies were moving away from us. This observation led to the development of the theory of the expanding universe.
The parallax should get smaller and harder to notice although in astronomy there are techniques used to find the parallax of stars by using the Earth's position around the sun to find the distance of the stars.