So, what did J.J. know, and when did he know it? And for that matter, how did he know?
Also, I'm relatively positive that JJ (in the sci-fi works he actually, well, worked on), himself, knew nothing (see Armageddon for sources) and that his script supervisors dealt with any discrepancies with reality JJ had.
[1] the reversibility it the hard part. Tech for halting metabolic processes irreversibly has been around for quite some time ;)
Closer than what? This system is significantly smaller than Firefly's. Or do you mean closer than this system is to Earth? Don't worry about that, since in Firefly it's one super-system with five main stars. http://i.picresize.com/images/2013/02/06/BMhCv.jpg It's about 55 light hours across.
The 'systems' in Firefly are really all one star system. The system includes a central star orbited by planets, four other stars, and a host of "protostars" (they really mean brown dwarves). I've tried, and can't imagine a scenario where, even if such a system could form, that it could be configured in this way. The barycenter of the masses of this system can't possibly remain in the central star indefinitely, for starters. And the whole thing sounds hostile to planets - I imagine them being thrown out of the system constantly. But if you accept that, and you accept travel at some fraction of c, then you wouldn't expect them to age much like they would traveling between systems.
In contrast, Proxima Centauri orbits from a distance of about a quarter lightyear, and we've found a single planet orbiting very tightly. We've also found a single planet around Alpha Centauri B, also orbiting very closely. There may be more we haven't found, but probably not nearly as many as in the Firefly system. Firefly seems to use the idea that more stars mean more planets, but more stars and planets during formation means more chaos, more things to swallow up or rip apart planets, and more mass to throw them out of the system.
I don't think the Firefly system is necessarily impossible. You can even construct models such that the white star is at the focus of all other orbits (you know, if you're the Alliance and you need to do that for political reasons). (An Earth-centric model of our solar system needn't necessarily be wrong in terms of its ability to predict the position of bodies in the solar system - It's just needlessly difficult and convoluted.) I just think the Firefly system is highly improbable.
If you travel at light speed from your own point of view you arrive instantly due to time dilation, so even if it takes years according to an outside observer (because the distance you're travelling is light years) you wouldn't age at all.
From a photons point of view, it is emitted and absorbed by its destination instantly.
My understanding is that Firefly does not have FTL travel at all, in fact that makes it rather unique among spaceship sci-fi. Also, they're in a single (though very large with multiple stars) system. They get around quickly because their ships are a lot faster than our slow-ass chemical rockets, but they're still traveling at sublight speeds, which is why it takes days or weeks to get places, instead of mere minutes (for example, at lightspeed, it would take less than 6 hours to get to Pluto). Notice that, in the show, they took paying passengers, and it took a fair amount of time to get between the "outer worlds". It was a lot like cargo ships of yesteryear, rather than modern airplanes, as far as travel time. They don't have tech to halt their metabolisms for the same reason we don't: they haven't invented it yet.