Does byakuya betray them?
No! thats his sister in law and he cares about her deep in his heart. And byakuya saved her life 4 times. He prmised his wife hisana (rukia's older sister) that he would protect her. Even though he told ichigo that he will kill her and wont save her because it's against the law, ichigo says if he was byakuya he would fight that law. So no i dont think byakuya has ever hurt rukia
Kenpachi has always wanted to fight byakuya. the first time they fight is when everyone thinks that Byakuya has turned on th shinigami and sided with the zanpakto instead and Kenpachi comes to fight Byakuya because everyone else is fighting zanpaktou. (anime: Zanpakto Alternate tale) the second time Kenpachi and Byakuya fight over who's going to kill/fight 10th espada Yammy. (anime: Fall of the Arrancar)
NO!!!!! No, Byakuya Kuchiki was married to his deceased wife Hisana Kuchiki who is also Rukia Kuchiki's biological sister, and Because Byakuya is part of a noble clan, he would never, and I mean 'Never' fall in love with a human who has no noble prestige, even though Orihime Inoue's name means 'Princess'.
No! Of course not! That's his percious sister-in-law! But he's very serious about his pride and doin' what the law wants. So if she is doin' somethin' to distrube that then he'll put a stop to it. In a couple cases Byakuya has actually saved her life (four times). I beleive the most recent one was when they were in Heuco Mundo, and Byakuya wanted to protect her from Evil Kaien. :3