@Duran
I will try to answer the first question briefly:
What beast does it state that gets thrown into the fiery lake with the false prophet?
Leaving aside Rev. 6:8, the next occurrence of the word θηριον is attested in Rev. 11:8. Here it is stated that after the 1260 days, a beast will arise from the abyss and destroy the two witnesses.
The beast from the abyss is mentioned in Rev. 17:8, stating that it goes away to destruction.
Thus, it may be considered that there is a direct causation of events: the death of the two witnesses is directly connected to the beast of Rev. 17:8. Its basic description in Rev 17:9-13 is identical (the angel describes the beast to John in general terms, without paying attention to details such as the crowns or the texts on the beast's body - cf. Rev. 17:3) with Rev. 13:1.
This is my basic view of the beasts of Rev 13 and 17. It is one and the same beast.
What other reasons can be given?
The next reference to the beast is Rev. 13:1. The dragon stands on the sand by the sea (12:18) and out of the sea comes (13:1) a beast that is strikingly similar to the dragon of Rev. 12:3, who is later identified (12:9) as Satan.
The dragon lends his strength, throne, and power to this beast (13,2). The whole earth admires the beast. In my opinion, the symbol of "earth" here is understood as a symbol of people and their hearts, which are like hard or barren ground. Or as such soil, which indeed bears fruit, but the cares of the world, the thorns and thistles, will destroy everything (Matt. 13:19-22). These are people on whose hearts the small seeds of the kingdom of God may have fallen, but they have not become true followers of Christ, good soil that bears fruit. When Jesus speaks in Matt. 10:34 about not coming to bring peace on earth, but a sword, He explains in the very next verse that by "the earth" here He means the people in the inner circle of true Christians (the real/symbolic family) who will persecute the true followers of Christ. So the land in Revelation has several meanings, and the above description applies - in my opinion - to Rev 13:3 (and of course other texts, but I don't want to go into detail).
The beast becomes an object of religious veneration (13:4), its power is limited to 42 months (13:5), and it will be so powerful that it will conquer the saints (13:7) and dominate all tribes, human communities, language groups, and nations.
In 13:11, it is specifically stated that another beast will arise from the earth. If afterwards (16:13) he is identified as a false prophet (cf. 19:20), then here again we are secting "the earth" i.e. these are the people who, though they could have brought forth a crop, did not bring forth any except thorns. Or the words of the kingdom of God "leaped" from them as from hard ground, or indeed, they knew something and were at first enthusiastic, but it quickly passed from them. So from this "habitat", people will be recruited who will form the "body" of the symbolic "false" prophet. They will speak like a dragon (13:12).
The false prophet (13:14) seduces, like the antichrist (2 John 7), so - if we understand the beast to be a rather political power, then the false prophet would symbolize a pseudo-religious organization. I don't think it's necessary to associate it with any particular church or religious system. It may be some ideology that will have pseudo-religious features, and that ideology will fanatically demand that everyone be devoted to it. It does not necessarily involve a god - see the conflict between Moses and Pharaoh, or Pharaoh's wise men or sorcerers (Ex. 7:11). I think it was more of a secular dispute - the description bears traces of "magic", but the reaction of the magi was entirely rational. I see it more as a conflict between religion (Moses) and the then, secular "science" (the Egyptian wise men) and it may be repeated again.
A false prophet, creates an image (εικων - the word then became the basis of "icon") of the beast. If behind the beast and the false prophet, stands the Dragon, then the image of the beast must be something supreme. Jesus used the term εικων when he held the coin where the image of Caesar would be. The image of the beast, then, must also be something similar. Some kind of icon. In my opinion, it is the Antichrist or the one who is "in the place of Christ".
There is a variant reading in the Gospels, especially in Matt 27:17, where Pilate asks if they want to release Jesus Barabbas or Jesus Christ? This sequence, this brief moment, if we figuratively "pause" it, then there, in those texts, in my opinion, we find all the actors: we find the beast (represented by Pilate), there is the false prophet (the high priest in Mat 27:20), but there is the murderer who participated in the rebellion (Mk 15:7). Barabbas becomes a symbol of the future Antichrist: he too will stir up rebellion in the "city" and will murder. Everyone will know that he is a murderer, but will prefer him to Christ...
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ugh, that was supposed to be a short text... I didn't write everything...