I like to think Wanda summoned (I wouldn't say resurrected, but summoned) Vision, so he isn't a magical illusion or the “piece of the Mind Stone that lives in” her. I think he IS Vision, yes, with a body recreated by Wanda but based on the code of his soul presented to her as a ghost (did that make sense?)
You can see this in the Agatha All Along end credits.
Following that same line, I think Billy and Tommy aren't just made of Chaos Magic, they aren't illusions either or “love persevering” (I'm not saying grief isn't love persevering, I'm saying those kids aren't). I think they're actual children of Wanda AND Vision.
Let's say Wanda summoned Vision's ghost and gave him a body made of Chaos Magic based on the DNA coded in his soul. Then, she combined a copy of her soul with Vision's (like gametes, but spiritual), they got two twin souls out of that and gave those souls bodies made of Chaos Magic (also based on the DNA coded in their souls). So their bodies are Chaos Magic, but they're based on their souls which are very real.
I spoke no spell, I said no incantation. You. You, I made from scratch.
So... there was conception, there was a nine months pregnancy (different than someone who had it easier because of television times... and Chaos Magic... But who am I to judge? Good for her).
Does that mean there was a father? No, not really.
Maybe it was a WandaVision-like situation. Maybe Agatha and Rio created a copy of their souls and fused them together to have Nicky; maybe his first cells were made by Rio, based on the DNA coded in his soul, out of the nutrients and stuff she herself reaped (not like: oh, she killed someone to use their body. But like: she took a little bit from every plant, small animal and even human she reaped; mixed it all together and created some cells) and they multiplied after that, and he grew up.
And no, I don't think he died young only because he was Death's son. Agatha herself said it:
(Which is heartbreaking, by the way.)
In those years, people died from things we experience as a simple flu. It was normal; sad, very sad, but normal.
So, no. He didn't die because of that (that's what I think, at least).