That last pic shows it's algae. Kinda looks like threads. It's thread algae. Pretty tough to get the species name. At least you know it's algae.
I like the way it flows in the current, a macro algae trait that is rare. Most (that are available) are too stiff to undulate sexily like that. If it showed up in my tank, I would keep it, but it may not jive with your goals for your tank.
If you want to get rid of it, I'd combine manual, stiff brush removal, outside the tank, then a bunch of Cerith snails to finish it off, inside the tank. They reproduce in your tank, giving a variety of sizes that can get into your rocks' crevices. Other herbivores that might eat it are tangs and urchins, maybe an angel fish. It's so cool to watch a tang forage naturally, in your tank.