From what we know, Gracie has been isolated from everyone outside her family all her life, friends nope, not until she met the MC, everyone she knew was part of the family, and even then she wasn't allowed to be a part of family dealings because her mother didn't want her to become like herself, sadly by doing that Gracie became more like her in the long run, which Cordelia has mentioned.
She wants to be a part of her family, especially since this newcomer, the MC, is already allowed to do all the stuff that would make her feel more like a family member, does she love violence, not from what ive seen(Except that one question incident during their "Mission"), she just wants to be a part of things, isolation from all you have ever known is making her react how she does.
She's learn't more from the MC about being a person, and everything else in the time he has been with the family then she had learn't in the years leading up to his arrival, except maths of-course, shes loves maths.
Isabella seems to be the most normal one in the family, then Gracie, then Wilfrid (I know strange that I put her before him right), then Luna and Cordelia, I dont know where id put Antonio in the normality stakes, we just dont know enough about him and his mother, but we do know they both have... Histories.
I dont think Gracie is a Psychopath, Autistic or anything like that, she just doesnt understand people, too isolated.
Just like I dont think Luna is a lunatic, considering what shes been through shes lucky she got the contact Gracie missed out on, if she hadn't had that human contact, she would be insane, or dead, or both.