Italo Calvino mentioned in his Italian Folktales that the silver nose was rare even in Italian tales.
But a silver nose was sometimes used as a prosthetic, when you lost a nose to syphilis. Hence, a silver nose is a sign of loose living.
"Solve et coagula" is the principle underlying alchemy: dissolve materials to their constituents and re-assemble these into something else.
Fulcanelli writes of this quote:
If you know how to dissolve the fixed,
And to make the dissolved fly,
Then to fix the flying in powder,
You have something to console yourself with.
This probably derives from the Greek coinage spagyria, which itself is supposed to come from 'σπάω' and 'ἀγείρω.' These words roughly correspond to "solve" and "coagula," or divide and join.
This word was used by Paracelsus, perhaps the most famous alchemist. I am using Andrew Weeks' translation, which I believe is from the (original?) German text.
This "falling from grace" story did not originate with Christianity. Take Tantalos for example, or Zeus banishing Hades to the underworld.
As for earlier "fruit-picking" mythology, there's the story of the Monkey King stealing the peaches of eternal life from the Jade Palace in Chinese mythology.
Leviticus is mentioned as a source on the scapegoat as noted by @Obie 2.0.
Then Aaron shall offer the goat on which the lot for the LORD fell,
and make it a sin offering. 10"But the goat on which the lot for the
scapegoat fell shall be presented alive before the LORD, to make
atonement upon it, to send it into the wilderness as the scapegoat.