Sparkle boy is about Damas's height and still mute (he uses Spargan sign language to communicate). He mostly works with animals and is an all-around skilled fighter; at this age (around the same as canon Jak) he would have already earned his full citizenship. He's got a good relationship with his fam, but while he has many friends none are as close as canon!Jak's relationship with Daxter.
He's got a lot in common with Jak; he's reckless and loves exploring on his own, and likes pranks and jokes. His channeling abilities are similar to TPL!Jak's; he's had much better teachers to guide him (allowing him to develop his skills more) but due to the relative scarcity of eco in this time he mainly relies on regular weapons and techniques when fighting, with channeling as more of a secondary/support ability.
Life in Spargus is rough, but of course the day-to-day hardships of the wastelander lifestyle are nowhere near as bad as what Jak endured in prison. Even if something awful did happen to him, sparkle boy is much better equipped to cope with trauma, and of course he has a strong support network to help him heal. He obviously doesn't have the same mental health issues as canon!Jak (fear of abandonment, PTSD, etc) and is a happier and healthier person overall.
The last two pics are time travel AU scraps. First is a concept for Dax and Damas catching glimpses of sparkle boy around Spargus and how they deal with that (considering they fought to bring normal Jak back instead of trying to change the timeline). The Kali page was for a prompt with the theme of possession; this will probably happen at least once in Echoes as her ancestry makes her more susceptible.
How would Damas and the mother handle any revelation that Jak is their son? Imagining Damas magically lives because boo canon
YES DADMAS LIVES!! I LIKE HOW YOU THINK ANON
For Damas, this would depend a lot on the circumstances of the reveal. He definitely has strong surrogate-fatherly feelings for Jak (especially after learning that Jak never knew his parents) and on some subconscious level he does 'recognise' Jak, BUT he's also not the type of person to easily believe a crazy story like time travel. He'd need time to process that information, and he might not believe it right away if the timing wasn't right.
He'd eventually accept Jak, of course, but it would always be a bittersweet thing for him; Jak grew up without a father and keenly felt that loss, and then he was put through so much trauma and suffering to fulfill a role others had pushed on him and which he was never given the chance to refuse. Damas would regret not being there for Jak through all of that, even though (at least in canon) it was entirely outside his control.
Kali would believe it right away (she's generally got a good feel for these things) and if she'd been around after Jak came to Spargus and had the chance to meet him she probably would have been the first to figure it out. But since she was away on her mission and didn't interact with Jak at all prior to the reveal, she'd need some time to get to know him; she's pretty slow to warm up to new people but once they'd spent some time together they would get along well.
There's some (very old) concept art for Brothers AU in this post (scroll to the bottom for the dadmas reveal sketches). Damas is at the metalhead nest when Kor makes the reveal, and he doesn't initially believe because the metalhead leader isn't exactly a trustworthy or reliable source of information.I've also sketched out the Fury Road dadmas reveal (including a later scene where they accept each other) over here-- in this one neither of them believe that they're blood relatives (Jak still thinks he was born in the past, while Damas is in a really bad place mentally and can't process the information) and the acceptance scene is more of a 'chosen family' moment. They don't come to realise it's actually true until a while after they've met up with Sig and Kali.
In Cascade... it happens under some of the worst possible circumstances (featuring unhealthy amounts of dark eco, many injuries of varying degrees of severity, and an attempted healing that doesn't quite go as planned). Also, Damas previously thought his son had died at the metalhead nest, which definitely doesn't help things go smoothly when he sees that Jak has the Kid's amulet.Jak doesn't meet Kali until after the initial dadmas reveal; it would be pretty close to what I described above (she learns who he is right away but needs time to get to know him).
And lastly, Echoes gets two dadmas reveals (because time travel) and the first one is actually what sets off the whole fic (it's literally the first scene so it's not really a spoiler). It starts out pretty similar to what I mentioned for Brothers (Damas is at the metalhead nest when Kor makes the reveal, and only Jak believes it) but then seeing Damas with his younger self prompts Jak to destroy the teleport ring so he can't be sent back-- which triggers a whole sequence of paradoxes with catastrophic consequences. In the final seconds before the timeline starts to eat itself, Damas gets to realise that Kor's story was 100% true and he just fucked up horribly. 8)Also, I've drawn the scene where Kali finds out (first image in this post) and she ends up being instrumental in helping Dax fix shit.
...Anyway, I hope this answers your question; it's really hard to give a simple 'they would react X way' on a topic like this.