If mercury core is made out of ironj right.
then if it would ever go into the sun wouldn't the sun die since iron kills it.
Nah, mercury is such a small object it wouldn't have much affect on the sun.
However more importantly iron does not 'kill' a star. I think what you are thinking is that if a star is very old and has fused most of the lighter elelments so that it is only fusing elements that result in iron then the sun will go nova. This is becasue when iron is fused it does not produce excess energy, so the outward pressure decreases and the star collapses. So it is not the exsistence of iron, it is the fusing of lighter element into iron that results in the 'death' of a star.