This also brings up something else. Do Kurono 1.0 and Kurono 2.0 have different souls? It could be that some time in the next 19 years, Kurono 1.0 dies and is the one used for the rebirth. Or it could be a combination of the two.
The soul explanation also brings up some more questions . Does it mean that there are a finite number of souls? Can a soul be copied for reincarnation to make up for a limit (Besides the cloning thing)? Is the soul of everyone always a reused soul, or are new souls created? Do souls eventually stop being used? Will these questions be answered in the remaining chapters? Probably not.
Also, if they can tell how someone will be reborn, then couldn't they know how the information they sent to Earth be used? Though I suppose it could be either they didn't care or it's like that whole "master of fate and tool of fate" thing in Dune.
As for how they get back, I suppose someone on Earth could use one of those alien transports to get to them, or there might be some small craft on that ship or station they can use to get off. The big problem for the first solution is how does anyone know to come rescue them?