The white tubes are pinapple sponges (Sycon genus), and they're harmless filter feeders - they tend to boom then bust in population before going away on their own. The other white thing in the first few pics with the multiple tentacles coming out of the central stalk looks like a "pest" anemone ("Aiptasia") - so you may want to remove that one (most would likely suggest you do).
That hammer is in bad shape, and the other coral visible in the background of a few of the pics is looking pretty rough too. My usual suggestions are to check the flow and lighting for the coral, but 0 Nitrate with 0.2 Phosphate seems off to me. So, here's a bunch of questions that could be useful here:
-What equipment (pumps, powerheads, etc.) are you using for flow in the tank?
-What lights are you using, and what settings and schedule are you running on the lights? Any idea how much PAR that hammer is getting?
-What test kits are you using?
-How big is your tank (what are the dimensions of the tank)? How old is the tank?
-What fish and inverts do you have in the tank? What are you feeding the tank and how often?