Even in the show the link isn't a constant thing it seems to fluctuate. So presumably the thought of it wasn't so huge that Stein noticed, or he couldn't interpret it. The show has shwon that it's not a psychic link in that they're literally reading each others minds. At most it usually just lets them feel one anothers feelings at times.
As for his body. It seems to have specifically been brought here to be ressurected. Presumably there's only so many moments in time that are ripe for it/areas that are conducive to it. I'm guessing the specifics if at all will be brought up in the future though it's hardly necessary.