Unless something weird happens, e.g. a currently-hidden AI keeps us from gobbling the stars, then an FAI once unleashed should be able to revive every human who's ever died, so even if you die before it's developed you should still be okay.
There seems to be rather a lot of information lost beyond the chance of recovery. The mapping of 'current world as best as the FAI could plausibly deconstruct' to 'possible histories that would lead to this state' is not 1:1.
The best I could expect of an FAI is the ability to construct a probability distribution over all the likely combinations of humans who could have lived and perhaps 'resurrect' rather a lot of people who never lived on the hope that it'd get most the ones who did live in the process.
There seems to be rather a lot of information lost beyond the chance of recovery.
Not if there are AIs out there in the universe who can catch the information and run it back to your FAI at lightspeed. And since our FAI can catch information about the causal past of other AIs that they'd otherwise never have been able to get back, it's even a clear-cut trade scenario. I see no reason not to expect this by default. (Steve's idea; I think it's pretty epic, especially if the part works where the AIs collectively catch all each others' quantum entanglements ...
What looks, at the moment, as the most feasible technology that can grant us immortality (e.g., mind uploading, cryonics)?
I posed this question to a fellow transhumanist and he argued that cryonics is the answer, but I failed to grasp his explanation. Besides, I am still struggling to learn the basics of science and transhumanism, so it would be great if you could shed some light on my question.