Purple spots appear to be the start of Coraline algae (which is good), leave it be, and eventually your rock will be nice and purple.
The green tuffs of algae looks like green hair algae (GHA). For that, pick up some more clean up crew (some snails and/or hermit crabs) and they'll eat it up.
EDIT: after looking at the pics more, I am more convinced that it is vermetid snails. The "sprouts" are feather dusters, and will typically are ok... the feather dusters look like a little duster at the end of the tube. Alternatively, they can be vermetid snails (they looks very similar). Vermetid's will send out long stringy spiderweb looking strings when you feed the tank. Typically they are also harmless, but if you get too many, they can bother coral or just look gross. You can get 1 or 2 bumble bee snails as they absolutely decimate those. But they can also eat up other beneficial worms. Personally, I always have 1 or 2 because I'd rather not have vermitids.
The anemone looking things is an aptaisa. Those things can and do spread quickly. I recommend using Aptaisa X or something to that degree and getting rid of it. Read up about it and dont just try to scrape it off, that can release more of it into the water column. If the plug is small (like your's) I usually pull it out into a separate container, use Aptaisa X and then rinse using tank water outside of the aquarium and put back in. You'll have to keep checking to see if it comes back, and repeat if that's the case.
CAUTION: the aptaisa X stuff will hurt the zoa too, and those can release palytoxin, so use gloves when handling just in case and don't let your hands soak in that container for too long. Wash hands thoroughly after and keep away from eyes while you're working with it.
As a side note, search the forum about black sand. There have been some reports of it containing iron (if I recall correctly) and it can leech into the water causing algae issues and coral problems down the line. So may want to look into swapping the sand out, or going bare t
