How is he able to interact with the users of the curse mark (like when Sasuke and Itachi fought and a version of Ororchimaru appeared out of a snake from the curse mark
Shifting Sands
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The curse marks are extensions of his mind and consciousness. He forges a link to himself on those implanted with marks. It's his specially designed jutsu/chakra that now exists within them. So he can see through them and has some level of awareness.
They're kind of like Voldemort's horcruxes from Harry Potter. Even if Orochimaru dies part of him will always live on through the curse marks and with the right jutsu he can be restored to his original state from them. The details of that vary though. He was only able to reappear from Sasuke when Sasuke ran out of chakra and was no longer able to suppress him. But another way is applying flesh with Orochimaru's DNA and performing a Curse Unsealing jutsu on the mark, which Sasuke did later on Anko.