[Lazy_Perfectionist]

Off the top of my head (accuracy not guaranteed, but close enough)

a). Starve two turns, get disease.
b). Come into play when storming a castle, but not when breaking siege.
c). wipe out other god's dominion. When every candle is white, you win.
e). It's all relative to other nations, so if nation A suddenly jumps ahead in research, then nation B might actually have their research (on the graph) go down. I'm not certain, but I don't think there is any absolute data available on this screen for other nations or victory goals.