Yuuka saw a ten year old girl with a dead, apathetic look in her eyes, like she would simply accept all misfortune without blaming anyone but herself, and Yuuka thought that was extremely attractive. She thought "I want this traumatized little girl to be mine". She's a predator. She also takes advantage of Aya's abilities regularly while still acting like she only half believes in them, just to keep Aya's self esteem down so she'll stay "hers".
Yuuka is a witch, like Michiru will be in the future, though less powerful. She doesn't remember them like Aya does, but she knows that the days repeat, and if Aya tells her about another version of the day, she can influence which day is chosen, or stitch together parts of multiple days to create new ones. That's why even though Aya woke up in her own room the day after Yuuka's accident, Yuuka was still alive. She died every version of that day except for the last one where Aya warned her, but she stitched the "Yuuka survives" part of that day onto another one where Aya never came over.
This is the main reason she actually keeps Aya around. It's just to protect herself. She acts disinterested whenever Aya tells her about the events of alternate "days", but she's always paying close attention to them. Purely on the lookout for bad events to avoid.
and the way she constantly manipulates Aya? God.
Not long from now she's going to have a shouting match with Aya where she gaslights her about her experiencing the days repeating,
even though, as mentioned, she already knows for a fact that Aya is telling the truth. She does this only to lash out at Aya because she's jealous of how close she's been getting to Michiru. It's not even genuine jealousy either, she just wants Aya to remain isolated and self-hating so she can manipulate her easier, and she's noticed Michiru changing that. Yuuka just wants to hurt Aya for going against her, and she does. Despite always rejecting her shameless advances, Aya cares for Yuuka a lot. She's been Aya's only companion and confidant for her entire life, until meeting Michiru. Yuuka's the only person who's ever believed her about her experiences. So when she lies that she never actually believed her, and was just humouring her like an over-imaginative child, Aya is emotionally devastated. And Yuuka did that to her intentionally.
So, She's been Aya's only friend and family since she was ten, she's made Aya completely financially and emotionally dependant on her, she's groomed Aya into being the self-hating apathetic "witch" she is now (purely because it turns her on), and she's just constantly emotionally abusive to Aya, manipulating her, lying to hurt her, lashing out at her for going against her, being kind only when Aya does what she wants, Etc.
Oh and yes, she did steal Aya's house key and get a copy made for herself. Aya's consent is not a thing she cares about in the least.
In conclusion, Yuuka is a dangerous, abusive, horrible person and Aya would be much better off staying far away from her.