@cyren-myadd to answer your questions about this au.
Quaritch wouldn't know if the kid is his. Back in the day, he nearly beat the shit out of Phillip Shaw for messing around with one of his female soldiers. So when he sees this kid with blonde hair, exactly the same shade as Phillip's pansy ass, he jumps to the wrong conclusion, assuming Phillip is the father of this little twerp. He also mistakenly assumes that Miles Socorro must have died on Pandora, because in his mind, there's no way a human child could survive on this planet.
I don’t see the RDA being too interested in who Julian belongs to, either. They're only focused on getting information about Jake Sully’s location. I can still see Quaritch taking Julian out of there like he did in the movie, but it's a manipulative move, not paternal in any way. And even if he does find out Spider is his son, he’d keep that information to himself. That’s a lot to process. However, he does plan on telling him once the heat dies down and Jake is strung up by his feet. Quaritch needs Julian focused, and he doesn't have time for emotional conversations when he's supposed to be tracking down Jake. He DOES start being a little nicer to Julian, but is still being manipulative to keep Julian reliant on him.
As for Norm, he would fight tooth and nail to find his pseudo-nephew. He’d even go so far as to join the battle in search of Spider, which leads to a confrontation with Quaritch, who’s holding Kiri hostage on the Sea Dragon. Before Quaritch can utter a single word about Spider’s parentage, Norm body-slams him from behind. When I say he’s willing to sacrifice himself and fight to keep that secret hidden, I mean it.
Kiri is freed during the scuffle and scurries away. Then it’s an all-out brawl with Norm clawing at Quaritch like a madman, because he’ll be damned if this piece of shit spills the beans and ruins Julian's life. Norm is injured, but he wounds Quaritch badly, nearly tearing his throat open and even trying to rip out his tongue to silence him.
(Quaritch still manages to escape, but whether or not he succumbed to the injuries Norm gave to him is unknown.)
Norm’s uncharacteristic brutality raises suspicion in Julian, who has never seen his guardian act like this. Maybe even Jake starts questioning Norm’s extreme dedication to finding Julian and fighting Quaritch like a goddamned Thanator. Norm stays tight-lipped, but I have this idea where Mo’at eventually spills the truth. She’s not stupid; she’s known for a while that Norm was hiding something, and she bullied Norm into letting her accompany him to the Metkayina's territory so that she could talk to the boy herself and do some extreme mediating. She's allowed this to go on long enough. No more.
She would have a long, serious talk with Jake and Neytiri, urging them to see Julian beyond his bloodline. I’m not sure how that will play out, but questions are answered, and Norm’s relationship with Spider is put to the test…this isn't going to end smoothly, and tensions are high, especially with Neteyam seriously injured.
But I swear this has a happy ending!
After the truth comes out, there’s tension and frayed trust. Julian pulls away from Norm, confused and upset, not just about the lie, but about having the story of his BIRTH constructed and shabbily patched together like an infected wound, and making him believe for YEARS that he was someone else's son!! This isn't just something that can be washed away with a kiss and a hug.
Julian's life was built on a lie, and even though Norm did this for his protection, it still hurts and makes him feel like an impostor.
Jake and Neytiri are stunned too, especially Neytiri, who struggles with the idea of this child, a friend and brother to her children, being connected to the man who caused her family so much pain. Jake feels betrayed, and he and Norm have a huge argument. Norm feels guilty, but is largely unrepentant and says some hurtful things when their argument gets vicious. "So what if I lied! You lied, too, Jake! You lied, and hundreds died! I wasn't going to let Julian hold your bag AND Quaritch's! Everything I did, I did for Julian!" THAT almost has the two go to blows, and Tonowari is forced to step in.
But it doesn’t stay that way.
Norm doesn’t give up. Even with his injuries, he shows up for Julian, again and again, not asking for forgiveness but simply proving, with quiet consistency, that he loves Julian. Neytiri remains distant for a time, but Mo'at and maybe even Kiri bridge that gap. Once again, Neytiri's trauma is real, and some time away from Julian AND Norm is needed for her mental health. It's going to take a year or two (maybe three) until Julian and Norm and the Sullys can look at each other without flinching. Kiri is the only one not majorly affected because she's attached to Julian and sees him as her full-blooded brother. It's the same for Lo'ak and Neteyam, but this information puts them in a really weird headspace.