Mary is the only woman on earth to have an offspring that could crush Satan's head. Eve had no such offspring. And not all women's offspring have enmity toward Satan. But one woman's seed did. Only one was up to that task. Jesus.
Having sex with humans is one way. Some feel that Satan's offspring pertains to the fallen angels that followed Satan when he was cast out of heaven. Some think it is those humans that choose to follow their Father Satan as his offspring. Mary's offspring is the only offspring that fits the description of the battle God was talking about.
How did Satan create a spiritual child with Eve? Did they have spiritual sex to produce Cain and then the rest of her children were ok because they belonged to Adam? Why would God protect a child of Satan's like He did Cain? God drowned the Nephilm. He owes them an apology is He kept spiritual halfbreed Cain safe, and killed the spiritual halfbred rest of them.
Satan is eternal. No one kills him. He is thrown into the Lake of Fire for eternity.
That is speculation, which the Bible seems to refute. If you continue the scripture, you'll see that God deals with all three inhabitants of the Garden separately. First Satan, secondly, Eve, and thirdly, Adam. The verses make the distinction. No where does it say that Satan entered Eve. She was tricked into sinning. God covered her sin. There was no need of an exorcism. Adam ate the fruit as well, but Satan didn't inhabit him either, and God didn't look into Adam's eyes when He was speaking to Satan.