Point 1: The difference between the pink unicorn (god) and quantum immortality is that while YOU don't understand either, there are plenty of specialists that DO understand quantum mechanics and there are scientific evidence of similar things hapening on a microscopic scale etc, while the religions simpy argue that it is beyond the understanding of any human beeing. You might not curently understand quantum mechanics, but spend a few years reading and you will.
Mind you, nobody actualy claim that quantum imortality spesificaly does work, only that it might or might not, and that it is fair chance that it does. As far as I can rmember that is.
Point 2: Again it might or might not be posible, but I find it quite plausible that it shuld be posible to fech the data if one has the infinite intelegence and power and science of post singularity entity. If nothing else than by some time travel-related method. (there are numerus posible reasons why it might be plausible to have a method of timetravel capable of observing the past, placing some sub atomic sensor in each neuron or something, or something completly different, but not able or not wanting to change it.) In any case, I find it decantly plausible that the past could be reconstructed if one had infinite-evrything, remember that it might be done even if it reuires the resoures of the entire universe for billions of years. By defenition the singularity after wich we can predict litle or nothing.