What are these and how to best clean them? - PNW

Hello! It's basically just the title. For the Mussel shell I'm mostly wondering what the tube things are. they are rock hard and all the rest of the black stuff on the surface of the shell is more flaky. it would be cool to clean it up a bit more but I'm not sure how I could without damaging it. For the other thing I don't really know at all. its just a chunk of something, like no rock or anything attached, so I don't even know what the base is, then there are the cup things and also the thin branching stuff in the last photo too. Thanks for reading!