They are distorted. Its just a very minor effect. Take your Andromeda numbers, the 110000 difference would be between the front and back, but that wouldn't be a visible distortion because it would be along the axis of vision. if you look at the difference in time between the center and the edges, you get something like sqr( 55000 ) + sqr( 2000000 ) = 4,003,025,000,000, √( 4003025000000 ) ÷ 2000000 =1.00037805353776129308527162 so the light on the edge would be .03% older.

Almost everything moves slowly compared to the speed of light. Typical velocities in galaxies are under 0.1% the speed of light, so things only move something like 100 light years or less over 100,000 years. That's not going to make a big difference if you look at something as large as a galaxy.

For relativistic jets from black holes it's an important effect and we need to take it into account.

You're right, and its shape IS distorted. The effect is just so tiny it's not noticeable. It helps to put some numbers on it:

• Our galaxy is ~87,000 light years across. So to an observer, the light from far edge would be 87,000 years older
• But it takes our galaxy 250,000,000 years to complete 1 rotation!! So you're right, there IS a distortion - the light from the back edge appears to be shifted by 0.0003 of a rotation.

The amount it has moved through the universe is just negligible compared to how fast light is compared to stuff.

The shape of distant galaxies depends on how their light is affected by gravity and space-time as it travels to us. One phenomenon that can distort the appearance of galaxies is called gravitational lensing, which occurs when a massive object bends the light from a more distant source, creating arcs or rings around it. Another factor that can affect the shape of galaxies is their relative motion to us. For example, the Andromeda Galaxy, which is about 2.5 million light-years away and 110,000 light-years in diameter , is moving towards us at about 300 km/s . This means that the light we see from different parts of Andromeda has left at slightly different times, but this effect is negligible compared to its size and distance. The Andromeda Galaxy appears as a nearly circular disk with two spiral arms , although its shape is also influenced by its interactions with two smaller companion galaxies, M32 and M110 .

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No because you can only see the light hitting your eyes now. not the light into the future or past. Its only if you leave a open camera and record so that as the earth moves the stars leave lines of where we were in position to where we see them.