Does any class assigned with Hope aspect start out with omnipotence or is that only reserved for Lords? If so, does that mean that Hope players aren't all omnipotent?

I think you mean Light, not Hope, Light is what’s usually associated with Omniscience. Full Omniscience, though, it’s hard to tell what Class, if any, would have it. I mean look at Doc Scratch, he’s the most Omniscient Being we know and he still has dark pockets in his foresight.