Thanks for the chapter!
I think Izuna is or at least related to Youkai in some way. First there's Yui who protected him so Izuna wouldn't be saddened like a caring subordinate/bodyguard who's stood by her for years. Then there's the weird look she gave him during the test, also she suddenly had something else to do right before entering his house. Just guessing but I think she might be part of a family or sect that handles and/or hunts down Youkai and/or the supernatural like an onmyoji. Finding out about her family duties would explain why she started distancing herself from MC to avoid any trouble she gets into from splashing onto him. Then there's the charm to ward off evil. Most students would've gone for a charm to help with studies, especially with MC's grades, while warding off evil would be because believe or suspect a bad spirit or something is haunting or endangering him.
As for onee-chan I think she's a bit of a tsundere who's unaware of how deep her feelings for him are. Granted she probably hates being sealed and ordered by the mother, but she definitely has some feelings for MC considering she got jealous and kissed him on the nose while tearing up. Not sure if little sister just trying to impress the mother or has feelings too or not.