There are many who mistakenly believe that Elijah came to earth as John the Baptist. But when the angel Gabriel spoke to John’s father Zachariah, he said that John would come “in the spirit and power of Elijah”, not as an incarnation of Elijah: And he shall go before Him [Christ] in the spirit and power of Elias [Elijah], to turn the hearts of the fathers to the children, and the disobedient to the wisdom of the just; to make ready a people prepared for the Lord.
Yes, John the Baptist was given a portion of Elijah's spirit because Elijah is to come BEFORE the DOTL (God's judgments) arrives. If Israel had of repented and accepted Jesus as their Messiah, Jesus would have returned and saved them from the Fourth Beast in 70 AD, but the Dan. 9:24-27 prophecy explicitly states that all these things must happen first, and Israel never repented, thus they have to repent before these 70th-week events can come to pass, thus God inserted the Church Age and saw Israel as Dead Men's Bones for nigh 2000 years. So, you are spot on, John was born of a Women, he was not Elijah returning, but Jesus states for all intense purposes, John did the exact same thing that Elijah would have done, but the people had a heart of rejection in them, in other words, Jesus was telling them John did the exact same thing that Elijah is going to do when he is sent back, IMHO, with Moses, whom we also see at the transfiguration on the mount with Jesus just before his death.
But the Tribulation and the Great Tribulation are in the future (possibly in the very near future). Which means that immediately after the Antichrist takes control of this world, Elijah will appear with Moses in Jerusalem to preach the Gospel to the Jews (Revelation 11) and turn many to Christ (even though they will be martyred).
Close, but Elijah shows up as Malachi 4:5-6 says BEFORE the Great and Dreadful Day of the Lord. You see, Israel has to repent first, thus they can flee to Judea BEFORE the A.C. conquers Jerusalem at the 1260 event, they flee at the (AoD) 1290 Event, which is 30 days before the 1260 event. The False Prophet (a Jewish High Priest) takes away the Sacrifice (Jesus Worship, not a meat sacrifice) and then defiles the temple by placing the AoD which is an Image of the A.C. in the temple of God. Thus the False Prophet (Jewish High Priest) does this 30 days before the Anti-Christ comes to power. Zechariah 13:8-9 says that 1/3 of the Jews repent and turn unto God and that 2/3 will not repent and will thus perish, but what does the very next verse say? Zechariah 14:1, BEHOLD the Day of the Lord Cometh !! Jerusalem then gets sacked. So, the Jews repent BEFORE the DOTL, and on that day, the day that God's Judgment starts via the first Trumpet, the Asteroid strike, this evil tyrant will use that asteroid strike as a cloak to go forth conquering amidst the chaos on this earth at that time. The Jews will thus flee at the 1290, which is 30 days before the 1260, the BLESSING is the Two-witnesses showing up at the 1335.
Everything else is pretty spot on, except its a Demon named Apollyon that ascends out of the bottomless pit, not the Anti-Christ.
God Bless....