What are these things growing on my toadstool?

[Pom]

I bought this toadstool (already attached to a piece of live rock) from diver's den and today I noticed all these things growing on the rock. What are they and should I remove them? Thanks.

 

[bull shark]

Are the tubes/stalks calcareous?

Is there 8 fold radial symmetry?

 

[trembz]

Looks like clove polyps?

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