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The thing people always overlook is that some of those names were given to the shapes that were seen thousands of years ago. And since then the position of those stars as we perceive them have changed quite a bit. And if they've moved in dissimilar directions, there can be quite a substantial change in the shape we see compared to what they saw. So the older the designation of a constellation is, the more it's distorted.
Due to the sheer size of space, this is most likely to have happened to stars closer to us (same thing as parallax effect, the same speed / moved distance moves something close more angular degrees across the sky)
No, it's mostly because of precession of the axis of rotation of the earth.
That just rotates the sky relative to somebody on earth, that doesn't really change how each star sign looks from earth if the stars are far away