The old fortuneteller was the closest thing she had to a mother figure and losing her in that crapsack village had to hurt. I have no idea how old she lived up to from her previous life, but she's pretty levelheaded and mature for a little girl so I think she had to have reached adulthood at least.
Broken slime? What is this cute creature? It may not win any awards for power but it sure is adorable.
So Ivy named herself? I guess she abandoned whatever old name she was born with and took up the name Ivy, for some pretty sad reasons but at the same time also a declaration of her resolve to keep struggling no matter how tough it gets going. A new name also works for basically starting over with life (it is very sad that she had to do this at a young age though).