@Velsy I don't think the demon "took" the cousin's place rather it is the cousin just in demon form (since you know, she's dead), that would explain why she doesn't leave because instead of a contract, she WANTS to stay, it's out of free will.
the uncle's in the hospital due to multiple self inflicted wounds iirc so maybe the summoning ritual for oneechan required blood or something and it was too much for him to handle
also just a theory but maybe because she's now a demon all the attributes she had when she was human is reversed. she was sickly and hated the sun, now she loves the outdoors and looks healthy af. she like to mess with people now but when she was a human she looked more like a caring person than a mischievous one