Please note the reason why Robo and Lucca are not listed is because when I'm in Zeal I always have Ayla and Marle in my party (I like their double techs). Ayla comes in handy when you're captured by Dalton because he steals and hides your weapons, but Ayla doesn't use a weapon, so she can still fight. ^_^
Schala loves her mother to death even though she is possessed by Lavos. Although she knows what her mother makes her do is wrong, she does not contradict her. Perhaps it is because she fears her mother will harm her, or maybe it's because she refuses to go against her mother's rule.
Her brother means the world to her. She would do anything to protect him even if it meant losing her life. Janus considers Schala to be not only his onee-sama, but his best friend (along with Alfador) in the world. Other than Alfador, she is the only one to whom he speaks.
Schala severely dislikes Dalton. He captures her new friends and even kidnaps her! Schala surely has the power to order Dalton around, but when she orders him to stop, he doesn't listen, and she doesn't try to stop him.
Schala doesn't realize the prophet is her brother all grown up, and she is never told. Because of that, she doesn't like him too much. He forces her to send Crono-tachi back through the portal from which they entered Zeal and seal it to prevent them from re-entering. Meanie! Don't treat your elder sister like that!
Schala respects the gurus and feels the only way to stop her mother is to bring them back. She asks you to save Melchior from where Queen Zeal banished him, the Mountain of Woe.
Because it is assumed that Marle is Schala's descendant and is also assumed that Marle and Crono marry in the future, this would make Crono Schala's -insert number of greats here- grandson-in-law.
Marle is Schala's great great great great (and a bunch of other greats) granddaughter, or so we are lead to believe because they both wear the same pendant. Schala doesn't get to know Marle very well, but she knows Marle is a good person willing to help save Zeal.
Schala is Ayla's great (times some big number) granddaughter; at least I think she is, but I'm only guessing that because they are both royalty of their respective times.