I suppose that depends on how you define "important". We're pretty important to ourselves, I suppose.

If everyone is important than no one is.

Depends on whether you are comparing everyone to each other or to something outside of the group of everyone. I could imagine we would say that everyone is important as compared to a typical stray photon with a duel-identity crisis.

False. A group's ability to survive a cataclysmic event, natural catastrophe, epidemic, or genocide depends on its size and diversity. There is safety in numbers and diversity.

One person being important doesn't negate anyone or anything else from being important. This is not the same as "everyone is special."

important with respect to the universe, not eachother

False dichotomy? :P