The worm is a spaghetti worm which are members of the Terbellidae family. The arms are tentacles that they use to sweep the surrounding area for food. The algae is indeed Halimeda as mentioned earlier which is a type of coralline algae found in the Caribbean. Healthy algae is green and will grow new "coins" from the tips of the furthest extension. When they die the calcium carbonate skeleton turns white and breaks down into sand.
Andy