
Allen P. answered 05/09/19
A Real Certified Teacher
This is a multi-leveled question but I will address the central part: "How far can a galaxy spin during that those few thousand years, and therefore how distorted are we seeing Andromeda?"
Not very far. The milky way is smaller than Andromeda, but it still takes it about 250 MILLION years to rotate 1x. So if the speed is comparable to Andromeda, and if you account for the size of that galaxy (approx 250,000 light years in diameter), that would mean that the light at the rear of the galaxy is 250,000 years older than the light at the front. With that said, due to it taking an estimated 250 million years to spin, in the grand scheme of things, you are missing 1% accuracy. So if light were to travel instantly, the picture would be only 1% more accurate. (Which on the scale of a galaxy that large with approximately 1 Trillion stars, means about 10 billion stars are out of place, but still its only 1% of the total count).