I would say Cordellia resents Teresse to some extent as... she will outrank almost anyone she'd be serving under and anyone looking into her circumstances from the outside would be wondering why she is even here. I imagine Cordellia has convinced herself to extra hard on her as she'd be doing it...
I can't help but be reminded of when Alucard fought that Valentine brother and the disappointment he felt when he couldn't live up to the hype when he went second form.
I wouldn't be surprised if the demon lord reputation and misdeeds have been blown out of proportion and was sealed for similar reasons to the resident witch. Here are my speculation on why the arrow was redirected: the pres has some sort of dormant power that would threaten the demon lord or...
Thanks for translation, if I remember correctly he was the guy that orchestrated the whole plot of awakening her as the Emperor so for her to strike him down for a minor misstep is quite amusing.
She's the protags estranged biological sister. He was kicked out of the family at a young due to shenanigans and fate conspired against the protag when she tried to rescue her from being overwritten? But ultimately failed to achieve her goal of saving her from the machinations of her family.