I've never felt my dreams to be so coherent between each other, but then there definitely are some continuities; sometimes it's overnight (i.e. waking up and remembering a dream, then dreaming something further involving it, or even telling the dream to somebody in another dream), but I probably wouldn't go as far as to try and extract different dimensions out of that.
As for lucid dreaming, in the few cases where I've managed it, I didn't really feel "omnipotent" but just grabbing whatever would come to my mind - then I never really had any idea of what I'd really want to do in that case... On the other case, I really enjoyed some actual dreams where I had superpowers (often flying which always felt amazing in my dreams), there were several dreams where I realised I was so overpowered that I was literally becoming an arrogant dick because I felt invincible.
