Why is this wrong: on ne pleure plus; c'est la vie
I think it wants the imperative mood, not the indicative. You wrote something like "we no longer cry..." This is indicative. Not quite the same as a command.
That would work. You could even add Allez, on ne pleure plus.
Why can't you say 'nous ne pleurons plus ...'
It means either "We don't cry any more …" or "We're not crying any more …", neither of which means quite the same thing as "Let's not cry any more …".
"Ne nous pleurons plus, c'est la vie." - wrong. Why?
It tries to make "nous" the Object of the Imperative: "Let's not mourn us any more …", which doesn't really make much sense.
You are using "pleurer" as a transitive verb, which changes the meaning to "to mourn/lament" and it does not make sense to mourn ourselves.