The 'coral' has concentric rings along the inside and is hexagonal along the ridges. I can not see anything that looks like modern septa costa lines though. I've been told it may be Favosites but i cant find too many accounts of them being found.
In regards to the bone, well it was washed out onto the beach, it definitely looks fossilized but I can't say much more about it.
Both pieces are around 5cm in diameter.