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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:
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:
It's generally suggested to get rid of hydroids, as they (like many corals) have stings - if the species has a potent enough sting, it can cause problems for you and your tank inhabitants.
There are a few species (like at least some of the Zancleid species mentioned above) that seem potentially harmless/worth keeping, but many are problematic, so removal at this point is the safer option.
Second digitate hydroids. Can be harmless/beneficial but can also be problematic...Welcome to Reef2Reef!
Those are Zancleid/Digitate Hydroids: