If we consider a point on the central part of a contracting object as observed from earth, the point is continuously moving away from us as the object contracts. Moreover, light emerges from a deeper gravitational well as the object contracts. So, shouldn't contracting objects show a redshift? And if so it should be less towards the edges than towards the centre, right?
Yes, they should. But do they, actually? That's the better question.
To have any appreciable redshift, the speed of the object needs to be huge. That will be a very short implosion. Also, there aren't many mechanisms that can accelerate implosions that much.
What I'm saying is - it's theoretically possible, but in practice you won't see it that often, if ever.
Sure. If the object is transparent to its own radiation, then you'd see blueshift from the other side, too. Again, this is very theoretical.