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Yes, the model can do a medium move when the model go into 'overwatch'. The model is then in a waiting position, keeping watch and is ready to fire whenever something is activating in their front arc. It isn't an oversight, it is small bonus you get when you use overwatch. Overwatch fire is not as good as normal ranged combat though. First, all can see where the overwatch model can fire (front arc), this can of course be good but also bad because enemy models can move around him or use mutations and gear to stop him from using his overwatch fire, but what makes overwatch fire way less good than normal ranged combat is that you can't push the attack and the push mechanic is very important in this game. Also, overwatch (i.e. sniper fire) is classically done with a rifle.

So, overwatch may be good sometimes, but normal ranged attacks are so much better so if you can fire immediately you do so (so you can push).

Does overwatch stop the other player's action?

Temporary. If the model being targeted by overwatch fire survives, he can continue with whatever he was doing.