Was just looking at the translation to "Love come down" and I think that it should be "inappropriate dream" instead of "rude dream". It's this word, and keep in mind the context: http://jisho.org/search/不埒
Correction for "Stone Cold": "damasareta basho" is "the place where I was deceived", not "a deceived place".
Corrections for "Eden":
"The dawn was tired of waiting" should become "comes the long-awaited dawn".
"Together with the baby's first cry" should become "since we first cried as babies" or even "since we first came to the world".
Correction for "neverending":
"After the street corner where I was supposed to catch up
I’m always laughing"
"I should have caught up at that street corner
but they're always laughing a bit ahead"
Correction for "Hikari no senritsu": (Or actually not a correction, just rephrasing the last part so it flows better)
Soon your hands will grasp
the eternal truth
But you think you don't deserve it,
so instead, with a loud voice,
you named this song "hope" and cried
It will surely reach
the heart of the person you're dreaming of
ari no mama de
yukeru yori mo tooku wo
The part that says "指を伸ばす生きる楔が欲しくて【Stretching out our hands wanting a living lynchpin】". 楔【くさび】 is translated as "lynchpin" but I think "lynchpin" should be "bond" in this context.