Well, the hint gave it away.
here and there:
you are still alive in the real world while sleeping, but you are also in a dream
moving and still:
you are still in real life but may be moving in a dream
seeing and blind:
you may see things in a dream but you can't see anything in real life
hearing and deaf:
you may imagine hearing things in a dream but you can't in real life
together and apart:
knowing and unaware:
you know things still, and it's a common belief that you can learn or work on things while you sleep, even though you are unaware of your surroundings
I am found by those who pretend they have already found me.
if you pretend to be asleep for long enough, you may eventually actually fall asleep due to resting for an elongated period of time
I am universal with infinite universes.
There are a potentially infinite number of dreams possible.
Without me, you die.
Without sleep, you die.
omega is the last letter of the greek alphabet. the last letter of the english alphabet is z. zzzzzzz is a common onomatopoeic effect to show someone sleeping or snoring.