The green-haired woman in the second season of Tokyo Ghoul was Ginko. She was one of the members of the Corpse Organization and also the classmate of the protagonist, Jin Muyan. At the end of the first season, she was portrayed as a very smart and ambitious character who wanted to become the leader of the ghoul organization. In the second season, she showed a more complicated and dangerous personality and had more connections with Kim Muyan.
It depends on personal preferences. Some people might think Tokyo Ghoul is better for its original story and character development. Others might prefer Tokyo Ghoul:Re for its continuation and new plot twists.
Season 3 of Tokyo Ghoul has a mixed relationship with the manga. While it retains some key elements, it also takes liberties that may not sit well with manga purists. Some story arcs are condensed or altered, affecting the overall coherence compared to the manga.
The Tokyo Ghoul manga is better because it has more detailed world-building and allows for a slower pace to absorb the complex themes. The anime may cut out or simplify certain plot points to fit the time constraints.