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Welcome, even though it's really a difficult topic to research.
Blackrock & Vanguard, specifically, are rumored to be majorly owned by Rothschild entities, but from what I see, due to the convoluted structure & the sheer number of companies the Rothschilds have set up over the centuries, I guess one has to be a financial expert w/ access to much better data to verify the connection clearly.
Since I am no finance expert, lots of digging on other pages (and lots of discarding piles of "conspiracy" info) would probably be necessary....
Just goes to say that factually answering your first question is probably not done easily (beyond what can be found written by people like Fulford et al.).