Regarding reproduction, I'm willing to write that off to advanced medical technology doing DNA repair. Most of the plot wouldn't be that different with slower space drives, so I wasn't too bothered by that either.

But fwiw, it turns out it is possible to get that level of rocket performance, if ToughSF got their numbers right:

https://toughsf.blogspot.com/2019/10/the-expanses-epstein-dr...

It wouldn't look the same and the power level would be higher than what all of civilization uses today, but the amount of fusion fuel isn't all that remarkable. The design uses helium-3, which could be collected in large quantity from Uranus and Neptune.