Why was HP so good despite being a Horcrux

Nature: Was it just down to genes?

Harry Potter was born to parents who were by nature good and kind people. Lily and James Potter fought in the Order of the Pheonix against Death Eaters. This would be risky, they would have seen other members die or be mentally disabled for the rest of their lives - the Longbottoms for example. James Potter was a trusting person, he let Dumbledore borrow his invisibility cloak despite it being a powerful, valuable, and irreplaceable magic item. Lily was a kind person this is evidence in her wanting James to stop his bullying and teasing of Severus Snape. Lily and James were very fond of their friends, risking letting them visit despite the couple being in hiding from Voldermort. They also entrusted their friend Peter Pettigrew to be their secret keeper; this led to the eventual murder of the Potters by Voldermort. James and Lily also made friends with their neighbour Bathilda Bagshot whilst hiding out in Godrics Hollow, a lady much older than the couple. The Potters humouring the seeming ramblings of an old lady spouting mad theories about the Dumbledore family:

"We had a very quiet birthday tea, just us and old Bathilda, who has always been sweet to us, and who dotes on Harry... Bathilda drops in most days, she's a fascinating old thing with the most amazing stories about Dumbledore, I'm not sure he'd be pleased if he knew! I don't know how much to believe, actually, because it seems incredible that Dumbledore could ever have been friends with Gellert Grindelwald. I think her mind's going, personally!"

— Excerpt from Lily Potter's letter

Despite Bathilda being mad as a box of frogs in Lily's eye they still enjoyed her company and saw her regularly. I imagine Lily and James felt it their duty to keep an eye on Bathilda being her magical neighbours and by this point Bathilda didn't seem to have much family left who would drop in to check on her. This fact is later exploited by Voldermort using Nagini to possess/impersonate the old lady; knowing how tempting a trip back to Godrics Hollow would be for Harry.

Nurture: early life

Also, Harry had some time with his parents before they were murdered, this is also illustrated in one of Lily's letters to Sirius Black - Harry enjoying his miniature broomstick around the house (a gift from Sirius). This tells me Harry was a very well developed baby or even a toddler before his parents were killed. During this time where babies are like sponges and learn so much from those around them, Harry was bound to pick up many kind and caring traits from his parents and watching their treatment of others.

We then come to the incident of the Potters being killed, specifically the "old magic" that Lily used to protect Harry. Did this old magic imbue Harry with any special traits? A good nature? Or maybe some sort of protection from the Horcrux fragment that was spliced into him when Voldermort attacked him? If the effects of other Horcruxes are anything to go by they are potent magical objects that affect the person just by wearing them around your neck for the day - the Salazar Slytherin's locket, later turned into a Horcrux by Tom Riddle. Imagine the power of a Horcrux you can't take off, that's inside/on your body and is with you your whole life. I think you would need more than a strong constitution to avoid the effects of such an object. Did Dumbledore realise Harry was a Horcrux the night his parents were killed and do something to help Harry? From the books, it is implied that Dumbledore didn't think of this until much later by which time the Horcrux would have had many years to do its damage.

Nurture: Dursleys

Did what Harry experienced as a child at the hands of his cousin, uncle and aunt colour Harry's feelings about treating others in the same way? That seems to be the case in the first novel where Harry decides to side with (not popular, poor and supposed blood traitor family) Ronald Weasley rather than the arrogant, pureblood snob Draco Malfoy. This is not typical for those who have been neglected, mistreated or abused in their childhood; they usually look for the same types of relationships in their own lives as they get older. Maybe the Dursleys treatment of Harry was so bad that he cannot standby and watch anyone suffer in the same way. This definitely would feed into later suggestions that Harry has a hero or saviour complex. I think it might also be described as a Robin Hood dellusion.

Harry's bad treatment at the hands of the Dursleys is fairly obvious; from Dudley spending time pinching his cousin as a baby, Harry living under the stairs with the spiders when we meet him; right up to them locking him in his room as a teenager. Was this immorality already part of the Dursley's or was it something that happened due to living with a Horcrux? Maybe the Dursley's are easily influenced people? Surely being a Horcrux would make you more easily bad than just living with one?

J K Rowling makes it clear that certain things cannot be done using magic like falling in love, bringing back the dead etc. Basically, you cannot do things that go against the laws of nature. So how much could be done to make sure Harry turned out a good egg rather than a rotten one?

Other things I would like to know:

Later life: Post Horcrux

Was Harry a different person once he is no longer a Horcrux? Did he have a calmer, happier, kinder personality?

Was he still powerful? He was effortlessly talented at the magic that Voldermort was skilled in, did that go away once he died and was revived?

Was Harry still good at Defence Against the Dark Arts? This is an area Voldermort was good at.

Was Harry still a parcel tongue? A skill Voldermort possessed and is assumed to have passed to Harry through his Horcrux scar from Voldermort.

Conclusion

I like to think being born to amazing parents who gave their lives to save their son made Harry naturally a good person and this along with his experience at the hands of the Dursleys made Harry an incredibly strong person. I think this goodness and strength enabled Harry to resist the influence of the Horcrux.