The old man is most definitely a self-insert cause there is no way any regular human being other than the author would think that something like "oops my bad I abandoned in an unfamiliar town a 7 year old child who I already knew was neglected and hated at her own home and thus became mentally unstable" is something forgivable that people would just laugh off as a silly mistake, on top of that the "old man" has the personality of a manchild trying too hard to act like a "cool adult". In "father takes care of child" stories you're supposed to admire the father, not feel like he's a selfish scumbag (even if he's weak physically he should have strong morals and personality ).