How did mankind get its sin nature?
This is a very fair question. After all, our sin nature is a foundational truth of Christianity, and without that, one might question if Christ's sacrifice was needed at all.
From a Theistic evolution perspective (well, at least this one, held by many Christians), our sin nature is absolutely real, as is a literal Adam.
Sin nature:
Well, the view that myself and many other Christians have is that humans evolved from earlier apes. At some point, God miraculously gave a transitional ape a soul. That was Adam. Adam rebelled against God, having the mental ability to recognize and think about God and the mental ability & freewill to reject God's command. That act was the fall. As a result of that fall, Adam's soul became vulnerable to spiritual death - and hence needed Jesus as a savior to grant eternal life of the soul in heaven.
The apes before Adam died, and without a soul, they just died. If we call Adam the first human, then he's also the first with a soul. Hence, there were no "humans" before the Adam, and hence no humans before the fall - though the apes just before Adam were very, very much like Adam physically, and like Adam, all experienced physical death, with their bodies rotting like any other animal.
All animals - human or not - experience physical death and their bodies decompose. Humans are the only ones with souls, and our souls can live on forever in Heaven, but only if we are saved. That's what Gen 2:17 is talking about.
This is in contrast to the view that our sin nature came from eating a literal piece of literally magical fruit, which one can get from a literal interpretation. Fruit isn't sin. Rebellion is sin. The fruit symbolically represents rebellion.
Make sense?
I would love to have somebody explain that to me if the creation/fall account presented in Genesis is a parable, myth or is allegoric.
It's poetic language allegorically giving us our history of rebellion.
Genesis 1 shows the reflexive poetry structure common in Hebrew poetry, and there are plenty of indications that this isn't intended as literal history, such as Hebrew puns. For example, the Hebrew word for dirt is "Adama". So God form a human out of dirt and named him "dirt".
Anyone who reads the story carefully can see the 1, 2, 3 - 4, 5, 6 structure of the days. That's classic Hebrew reflexive poetry.
Asking to understand the other person's view is always helpful. You don't need to agree to see how it works - just as I don't need to agree to see how a literal interpretation can be seen.
It's too bad other posters have not tried to directly answer your question from a Theistic evolution perspective.
In Jesus' name-
Papias