OP not only misses important points but has a number of inaccuracies eg Solomon leads to Joseph not Mary and Nathan to Mary per Luke. The distinction is important the royal line from Solomon was cut off at Jeconiah/Coniah at Jeremiah 22:28 thus Jesus could not be enthroned as the King of the Jews by that lineage, but he is of the House of David via Solomon and Lineage through Nathan.

Setting aside for a moment satan == lucifer. Without doubt satan is the serpent of Genesis 3. I like your Eve spiritually ruined then Adam physically ruined for God to reverse that in Christ as physical first then spiritual - 1 Corinthians 15:45/46 alludes but is not explicit as you have explained. This is true of balance we see in many places with God reversing action x with action b.

Re satan is lucifer, nowhere in the Bible - as far as I know but always happy for a source - is satan called lucifer, Revelation 12:9 Great Red Dragon - Serpent of Old - Devil and satan no mention of lucifer. Jesus said 'I saw satan fall like lightning' and not 'I saw lucifer ...'

Isaiah 14 - those translations which say Lucifer are personifying from 'O Day Star son of the Morning', in the Hebrew. This would place this individual on a level with Christ 'Bright and Morning Star Revelation 22:16 thus he becomes the Anti-Christ. Also possibly Job 38:7 'when the morning stars (plural) sang together.

Isaiah 14:16 says this individual is a man, and that he was cast out of his grave v19 - much of the passage speaks of the individual as a man, as for the 'I wills ..' reflect was was happening at Babel. There is also much which speaks of heavenly matters.

As best my research ever reached was Jerome's vulgate translation as Lucifer in Isaiah 14.

If Satan is the anti-christ we then have issues with the Beast from the Sea who we generally call the anti-christ since he is empowered by the Dragon/satan, Revelation 13:2-4.