Your cleanup crew knows when a coral is on the way out and since hermit crabs are opportunistic eaters they will feed on dying coral just like bristle worms even Nassarius snails.
It looks like an LTA and it looks like the size has been drastically reduced which usually indicates that he's slowly starving. Anemones do inflate and deflate but in the first photo it isn't deflated. To be able to help you we need to know the parameters and what type of lighting and how many...
Yes corals adjust to their conditions (lighting/flow) moving them often is not a good thing and can lead to stress,I would suggest finding a good spot and leaving them there.
In captivity you'll find very little if any zooplankton in the water column even in mature tanks in my experience. If they hunted pods like wrasses then yes they would have plenty of natural food to sustain them but that's not what they do.