They are not FTL, they are lightspeed.
They managed the computers through quantum entanglement.
It's not god powers, imagine 21st century humanity vs middle ages humanity. Like Arthur C. Clarke said, "advanced enough science is no different than magic" or something along those lines.
My point, though, is that we're making up a fantasy world where the impossible is possible, and a bleak universe isn't more "realistic" than a hopeful one. It bothers me that people try to praise the "realism" in these books. They might as well have just sent Frieza to blow up the planet. It's within the same realm of possibility.
Devoured all three books - really interesting hard sci-fi, although as noted by others, the first one took a bit of effort to work through.