I'm not sure on this one, though I've seen similar things a couple of times now - it should be harmless.
The brown is a sponge - it should be harmless/beneficial. The white structure on the right is a hydroid colony; unless you're feeding lots of pods, rotifers, brine shrimp, etc. it should go away on its own soon.
Yeah, most likely tunicates; harmless filter-feeders. I would guess
Eusynstyela tincta, but I would need clearer pics to feel more confident there.
The whitish stuff to the left of the purple and orange is probably a sponge; the purple and orange are more colonial tunicates - these ones are a kind that may potentially become invasive (with some species being able to grow over and smother healthy corals), so I usually suggest these ones be isolated on their own rock separate from the main rockwork so you can more easily control the spread. They neat little critters though.
If you want to try and help the tunicates do well, offering some phytoplankton would probably be wise. Isochrysis and Rhodomonas or a blend containing at least one of these would be my first choice. For a more intensive diet that would likely show better results, see "Table 3" in the link below:
I agree this is a Calliostoma species - I'm not familiar enough with the genus to feel confident in my ability to ID them at the species level just yet (the genus has a lot of species in it), but the Jujube Topshell is a solid guess.
These species do seem to prefer very large substrate to grab onto (be it rocks, coarse gravel, corals, or macroalgae blades), so I probably would move it off that fine sand.
As mentioned, the first one is a Red Mithrax crab - it should be as safe as an Emerald Crab to keep. The other one is not reef-safe, but if you want a proper ID on it, I would a pic of it's back/top (the dorsal side).
