Please find my comments in italics
The possibility of sin if it entered the world through man, has it entered the heavenly realm through the angels?
There is no sin in heavenly realm. Sin entering heavenly realm through the angels is out of question and beyond anyone's imagination. Angels who rebelled against God were thrown out of heaven. God dwells in the third heaven.
"I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth;) such an one caught up to the third heaven" (2 Corinthians 12:2
“And there shall in no wise enter into it anything that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life” (Revelation 21:27)
How can we say it cannot enter the heavenly realm? Angels stay in heaven. They rebel there. When they sin, that is when they are cast. That would mean based on the being, sin can emerge wherever they are placed. I am talking about the current heaven and all its level.
I have read the verse of Ap. Paul on the third heaven. If the Lord stays in the third heaven? Who stays in the first and second? How many more would be there?
Revelation 21 talks about a new heaven and earth, where this would not happen.
Is that why, there is there is a mention on new heaven and new earth. If observed, sin entered the world and not earth. Satan offers the Lord - the world and not the earth in the temptations. So earth by nature is not corrupt, but corrupted by man (Ecc 7:20). Still there is a need for a new one. So, why a new need for new heaven?
When Adam sinned he lost dominion over the earth. The earth is cursed for man. God has full control over all events but He will not interfere until the time is ripe for full destruction. Jesus had cast away demons, but never did He destroy a single one fully. Example can be seen in Matthew 8:28-31. Earth will not have renovation as some teach. Satan is the prince of the air. It is this portion, where Satan is the prince of the air, and the earth that will fully be destroyed and not God's abode, which is third heaven.
"Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience" (Ephesians 2:2)
"...The heavens shall pass away with a great noise, and the elements shall melt with fervent heat..."(2 Peter 3:10)
"For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind". (Isaiah 65:17)
So you agree with me there is a need for a new heaven and earth. Which is evident in passages and also clearly substantiated in Revelation. So we are in agreement here on earth. But heaven, if we go to what was stated earlier, then heaven is pure since all defilement are cast down. It need not be re-created, but it still passes as per the scriptures. Are you sure about the understanding that God stays in the third heaven only? Wouldn’t that be re-created as well. Yes, I agree with you on earth not being modified, that is wrong teaching.
Elect angels ( I Tim 5:21). Are they different from angels OR are they only a differentiation between angels of heaven and fallen angels?
The elect angels are those whom God preserved as ministering spirits to minister those who are heirs of salvation. God controls them and therefore they can never rebel against Him. They are ministers of flame of fire. The children of Israel received the Law by the disposition of angels.
"Who have received the law by the disposition of angels, and have not kept it" (Acts 7:53)
And of the angels he saith, Who maketh his angels spirits, and his ministers a flame of fire. (Hebrews 1:7)
Who maketh his angels spirits; his ministers a flaming fire: (Psalms 104:4)
Are they not all ministering spirits, sent forth to minister for them who shall be heirs of salvation? (Hebrews 1:14)
We should distinguish between fallen angels and evil spirits. Satan has a kingdom and he has evil spirits under his control and all of them are in the world right now and he is the prince of air.Evil spirits are not bound in chains but they are active now.
"But when the Pharisees heard it, they said, This fellow doth not cast out devils, but by Beelzebub the prince of the devils" (Matthew 12:24)
Fallen angels are those who rebelled against God and are chained and delivered to darkness reserved unto judgment. They are never released and never had they come out from abyss. The word used in 2 Peter 2:4 is “tartaroo” ( also called "Tartarus") Greek Strong's number 5020. This word is never used in the Bible again anywhere. The word is borrowed from Greek mythology by Jews. The meaning of which is lower part of the earth, abyss or hades (Gehenna), where wicked are imprisoned and tormented.
You are clear to a great extent. But then let’s take the context of Revelation 12:7-9 – they fight above and then are thrown down to earth. Then in Revelation 20:2-5, they are in the pit. So they are freed, isn’t that right? This is then the future, of them being released and coming up and finally facing the eternal battle?
And it shall come to pass in that day, that the LORD shall punish the host of the high ones that are on high, and the kings of the earth upon the earth. (Isaiah 24:21)
Host of the high ones refers to the objects of idolatry which are sun, moon and stars; they are not the angels as some suppose. The sun, moon, and the stars will be darkened.
"Immediately after the tribulation of those days shall the sun be darkened, and the moon shall not give her light, and the stars shall fall from heaven, and the powers of the heavens shall be shaken" (Matthew 24:29)
The “kings of the earth” refers to the wicked powers that abuse their authority to harm or persecute the church. They are those who did fornication with the whore of Rome. They will make war with the Lamb, who overcomes them (Revelation 17:2)
Host is not used for the term of non-living but of the living. Sun Moon are all creation but don’t embody the living. I presume the term is for the devil who was also a host of the heaven.