Not sure on the black dots (probably a pod of some variety, but microscope pics would be needed to say for sure). For the string though:I’ve found a string with little tentacles on my zoas but also very little black dots running fast on them as well.
Those are Digitate Hydroids (definitely a Zancleid hydroid [taxonomic family Zancleidae], possibly a Zanclea sp.) - there's evidence to suggest that they're actually beneficial to the corals they grow on;* I don't know if they'd sting fish that get too close or not, but it is a risk - similarly, they may spread and cause issues by growing too numerous in the tank and possibly posing a risk to other tank inhabitants.
I know @Reefkeepers Archive had a colony of these - I don't know if they've caused any problems for them or not, but if they still have the colony, they'd have ~5 months of experience with them to relate.
*Source: