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It might be a Tetralia sp. These crabs lives in acroporid corals in a symbiotic relationship. They are thought to be host specific, discriminating between species of Acropora. They are largely harmless to the corals themselves and may even keep the corals healthy.

They do need light to do well since they harbour photosynthetic zooxanthellae.

The first image looks like a Banded Bead Anemone. Possibly Anthopleura handi. Their natural colour is as in the image. They may sting your fishes and they also givegive birth to live young. If you do not want an infestation, best to remove it.

I think this crab will eat almost anything that it can grab with its pincers. Not sure about corals though. It is also a very strong crab and will not hesitate to do renovation work in a tank once it grows larger. I will suggest removing it as soon as one finds it.

Stone or Thunder crab(Myomenippe hardwickii). An agressive crab.