As for Zhou Heng taking away the fragment of the blood-colored greatsword, Han Yiyao didn't stop him, and she said she wanted to share some of the benefits.
It's true that she was the one who broke the door, but she used Zhou Heng's magic artifact, and the blood-colored greatsword was cut by the Black Sword, which had nothing to do with her! If it weren't for that, she would have been enslaved by the blood-colored greatsword by now!
Besides, even a peerless magical instrument, when broken, is just precious material, with its value decreased who knows how much.
She wasn't an unreasonable person; both morally and logically, she had no reason to intervene at this time.
However, she had originally thought that the legendary peerless magical instrument was hidden here. She didn't expect to have hoped in vain, nearly losing her life! If she had entered alone, it would have surely been a certain death.