1) The Brotherhood spent quite a while chillin' at HELIOS One, trying to unlock a way to active ARCHIMEDES. Their best experts, however, couldn't do it. Then you walk in and use the two terminals (even Fantastic knew you had to do that), waltz through some security robots (that weren't active then the BoS controlled the place) and then choose "reroute power to Strip, Freeside, or Orbital Laser?" I guess that what's on-screen in-game isn't what really appears, but you can do that no matter the Courier's science or intelligence.
2) What are folks in the bunker eating (heh, reminds me of Fallout 3)? It's quite a plot point that they don't take in anything that's not weapons tech (and have no interest in something like vault 22's food production), and they don't want to give any laser toys away. I guess they could be selling Guns, though they certainly aren't producing those. If they aren't traders, Veronica does act like she's a scavenger/prospector, but from what I can tell those don't make enough to feed a bunker.