What Would a Normal Harry Potter Look Like?
Harry's life is not normal. He was an orphan whose survival was based on the existence of a prophecy and Lily's sacrificial protection, and he was abused by his aunt and uncle for ten years. His overall behavior and personality were shaped by his upbringing and the way the rest of the wizarding world treated him due to his celebrity status as The Boy Who Lived.
What I wonder is how Harry would have developed if he wasn't orphaned and abused, and if he wasn't the Chosen One? How would he turn out if he was a normal child, with no prophecy, no sacrificial protection, and no celebrity status? And how would that change the events of the seven books, assuming Voldemort has been defeated prior to his first year?
I am of firm opinion that a Harry Potter who grew up as a normal kid without Dursley upbringing, non-celebrity status, no prophecy and no sacrificial magic would've been what Snape always assumed, a second coming of James Potter.
He would've been raised by James Potter predominantly alongwith Sirius Black and Lily. He would've been spoiled rotten, taught Slytherin prejudice since a young age, grown up with sense of entitlement and privilege and would've been never denied anything within his demands.
He would've started at Hogwarts with House Gryffindor as his default choice, probably formed a group like Jr Marauders or something, would've eventually become a bully and more magically competent than canon Harry (only initially). Assuming Voldemort got defeated without a prophecy, series would've become a slice of life drama focussing on Harry James Potter, Jr marauder extraordinaire and pals.
What @naaga said or the complete opposite.
Children do not always take after their parents and I know this from personal experience as I'm the exact opposite to both my parents in everything I can think of our only similarities are in some mannerisms. I imagine that if Harry did not turn out a carbin copy of his father, he would be rather ashamed of his dad's behavior, his jokes and pranks (as are most kids) but he would be a happy and confident boy.
A fanfic example I can give is Harriet from "Pureblood Pretense," she is a potions prodigy and idolizes Snape. Obviously, her dad doesn't really understand that and Harriet notices that it kind of hurts or disappoints him that he isn't her personal hero but she is still loved and he does accept her as she is. She isn't arrogant but very mature and intelligent, she is spoiled in the sense that she gets what she wants but that usually refers to means to further her knowledge so it's definitely not like James but I also don't really know (don't remember exactly) how bad Snape's relationship with the Marauders was in that AU as Lily didn't go to Hogwarts and she is practically the reason for their feud. So it is possible that James wasn't such a jerk to begin with but a decent parent is expected to grow out of that unacceptable behavior and mature.
I feel a little conflicted about how Harry would turn out, but I'll do my best to work my way through it:
From what I can tell, canon Harry tends to mirror the people around him and treat people based on his first impressions of them. The Dursleys don't like him, so he doesn't like them. Hagrid likes him, so he likes Hagrid. Hagrid doesn't like Slytherins, so Harry doesn't like Slytherins. Draco doesn't like Hagrid, but Harry likes Hagrid, and so doesn't like Draco. Etc.
I think that James would spoil Harry and be the "fun parent", letting his son get into mischief as he did when he was younger and just saying "Boys will be boys". Conversely, I think Lily would be the strict parent and try to stop Harry from getting into trouble, which would undermine James's previous permission for the behavior. This could be a major point of contention between the two of them, and they would get into arguments until one capitulated. We know that Lily is unwavering in her principles, so James is more likely to "give in" (based on canon observations, he'll likely lie and teach Harry how to be more discreet about his mischief). I think Harry would prefer James to Lily, as he feels James grants him more freedom while Lily is restrictive.
Assuming Snape works at Hogwarts and teaches Harry, he'll keep his eyes on him at all times and be paranoid (for logical reasons) about Harry's behavior. If Harry were to be caught, I think Snape would come down hard on Harry, which may prompt Harry or Snape to write to his parents and complain about the punishment. While Lily wouldn't approve of Harry's behavior, she may disbelieve Snape at first due to being a protective mother and her probable dislike of Snape, but she would most likely believe him if there was substantial evidence (perhaps the cloak of invisibility). This would probably cause an argument at home between Lily and James.
I think a turning point for Harry would be finding out how James behaved as a student. In canon, we see that Dudley's change of heart came from a Dementor attack, where instead of making Dudley relive his worst experiences (which were far and few between due to his upbringing), he relived the bullying and hurt he put on Harry and his other victims. Whether Harry is a bully or not is irrelevant; if Dudley of all people can have this epiphany, I believe Harry can as well. He'd probably start thinking more about what sort of person James is and how his own actions reflect his father's.
In a Potters survive universe, I don't see Severus Snape staying to teach, perhaps not even becoming a Professor.
No prophecy/Voldemort defeated before it – No defection – Punishment for Snape based on crime (I don't think he would get much, despite how many fics love to torture him post first war, he was spy based DE whose only crime was being a DE officially, Karkaroff elaborated on crimes of others yet could only come up with that against Snape and most of the people didn't know he was a DE) or escape punishment entirely.
Depends on the circumstances, but as this topic is about Harry, I'll keep it short.
Dumbledore might call Snape out during the DADA interview and threaten him with Azkaban unless Snape spied on Dumbledore's behalf.
Threatening others is not Dumbledore's style, he is more of emotionally manipulative. Here, Snape didn't have any reason to turn, his only reason being Lily's life whose life is pretty secure.
Most Dumbledore can do is calling out Snape during the DADA interview like he did to Riddle in the past.
