For your first question, I think my answer might come to you as a surprise.
The Two Witnesses are the Gentile Church. This can be a lengthy explanation so please bear with me. I will describe it how in the order it is written.
Rev. 11 starts out with measuring the temple. The obvious reason for this is because it is saying that the temple was going to be destroyed. Therefore, the new measurements had to be laid out, like what Ezekiel 40 did. The reason for this is because the Time of the Gentiles were beginning. To get that, you'd have to go back to chapter 10 and see verse 17, where John is commissioned to begin a new prophecy about many peoples, languages, nations, and kings; the Gentiles.
The prophecy of the Two Witnesses is inserted between the sixth and seventh trumpet blasts. The sixth trumpet is the destruction of Jerusalem and its temple. (I can explain the trumpets in another thread. I just want to get through this one without getting off topic.) From Jerusalem's destruction, the kingdom of God was given over to the Gentiles. (See Mt. 21:42-45, Mt. 22:1-14, Lk. 21:24 for more detail.) So, the Two Witnesses are not Jews, like the 144,000 sealed before Jerusalem's destruction. They are Gentiles.
These Two Witnesses are commissioned AFTER Jerusalem is trampled underfoot by the Gentiles. So, post-70 CE. They are the two olive trees. This is taken from Zech. 4, which was written about the rebuilding of the second temple by Zerubabbel the governor and Joshua the High Priest. The lampstand in that chapter represented the second temple. The two olive trees had branches that extended out and poured oil into the lampstand, signifying that Joshua and Zerubabbel would rebuild and reconsecrate the temple. When Zechariah asked what the olive trees were, he was ignored by the angel. When he asked what the branches were, he was told that these are the two that stand before The Lord of hosts. That's our tip. The two olive trees are priests, like Joshua, and kings, like Zerubabbel. This is a repetitive theme in the book of Revelation to signify the saints. (See Rev. 1:6, 5:10, 20:6)
These are also two lampstands, which we already identified were temples. But we know that the temple was destroyed. So these two witnesses are the temples. These are what many today call The Church. (But so much more than that!) They are built upon the prophets and apostles, with Christ being the chief cornerstone, into a glorious temple (Eph. 2:19-22.)
Their prophecy is the witness of the Gospel to all nations. (Mt. 22:10) Their witness is like fire to wood, convicting of evil; like when the Christians stood up to the Romans at the Tribune, like what happened to Smyrna. (Rev. 2:10) They would receive words from the Spirit and those words would pierce the heart.
Now you asked about Moses and Elijah:
They are like Moses and Elijah. This can be hinted at by the plagues they cause, similar to those caused during Moses' and Eljiah's ministry. But more than that, their goal is the same. They keep the commandments of God and hold to the testimony of Jesus, like Philadelphia did. (Rev. 3:8) This is also a repetitive theme, as you can see. Revelation 12:17 shows it in plain language. The Gentile Church was to keep the teachings of Christ and hold to His testimony (Rev. 19:10.) Like Moses, the Church kept God's commands (the teachings of Christ, the New Law). And like Elijah, the Church preached to the pagans and unbelievers who the One True God was. Not only that, these live out the blessings of God (Deut. 28:1-14) so as to inspire the Jews to jealousy, by which they would throw off the curse of the Law. (Romans 11:11)
As Luke 21:24 and Romans 11:25 shows, the Times of the Gentiles would eventually come to an end, with Jerusalem receiving their Lord again. When that happens, the temple that was measured will have been rebuilt in Jerusalem, fulfilling what Paul looked forward to in Romans 11:25; All of Israel will be saved. The kingdom of God would finally produce fruit in Jerusalem and bless the name of the Lord. Christ's would then cleanse the Jews and Jerusalem of all unrighteousness, allowing the Holy Spirit to enter the people and make them God's temple. Then the Two Witnesses will have then finished their testimony.
Another interesting observation: The Two Witnesses are resurrected in Jerusalem and the city praises God after that point. Paul also notes that if the rejection of Israel mean salvation to all nations, then what would Israel's inclusion mean but resurrection of the dead? And so we have it. The Two Witnesses are the Gentiles, living out the promises of God in the kingdom of heaven. They do this in an age called The Times of the Gentiles and will continue to do so until the fullness of the Gentiles has come in (Rom. 11:25.) Then the eternal Gospel will have been preached to all nations. (Rev. 14:6)
I hope you found this research helpful!
Anything short of the glory of God is sin. Flesh is sin. Flesh is corruptible and has no light in it. All must die for all have come short of the glory of God. Enoch and Elijah have not died. The two witnesses will die. Flesh and blood can not inhabit heaven forever for it is short of the glory of God. Therefore, the two witnesses will very likely be Enoch and Elijah.
God bless Bluefinger