At some point the show has to explain what happened to Root from the age of 10 when Hannah was kidnapped and murdered to her losing her mother (she stayed and took care of her mother until she died, and then how she became an assassin. There are gaps there. If we follow the timeline, Root is 3 years younger than Hannah meaning when Carter and Reese went to Texas, they thought Root was Hannah and they estimated her age to be 35 but as it turned out Root is Samantha Groves, whose mother died 10 years earlier, so that means she left Texas at 22 after her mother died. And I don't think she was killing already at that time. Something happened to her that she lost all human compassion or lost her trust in humanity. Obviously she has feelings because she took care of her mother. I don't think there was ever a father in the picture.
I do think she was already a hacker even then in Texas and I think that is how she paid for her mother's medical bills. I think he and her mother were poor and came from the other side of the tracks based on how that Librarian detest attitude towards her. She was probably teased a lot as a child for being poor. Somehow, I think she was recruited mainly as a hacker but eventually, became a hacker by getting tangled in that web.