Angels are ministering spirits created by God before He created the world (Hebrews 1:14).
Angels existed before humans. They are called sons of God.
God says in the Bible:
"Where were you when I laid the foundation of the earth? ...
When the morning stars sang together
And all the sons of God shouted for joy?" (Job 38: 4,7)
Angels are all male, because only the male pronoun is used when referring to them in the Bible. Just as with God, the male pronoun is always used, so it is with angels.
Their appearance
Not all angels have wings. In the Bible, the classes of angels with wings are cherubim and seraphim. Cherubim were depicted with two wings in Exodus 25:18-22 on the mercy seat of the ark, and in Solomon's temple in 1 Kings 6. But some cherubim have 4 wings (Ezekiel 10:21). And seraphim (another class of angels) have 6 wings (Isaiah 6:2).
However, many angels (who are not cherubim or seraphim) don't have wings. They often appear looking like men to people on earth.
For example, the Bible describes the appearance of angels after Jesus' resurrection.
"And behold, a severe earthquake had occurred, for an angel of the Lord descended from heaven and came and rolled away the stone and sat upon it. And his appearance was like lightning, and his clothing as white as snow." (Matthew 28:2-3)
“While they were perplexed about this, behold, two men suddenly stood near them in dazzling clothing; and as the women were terrified and bowed their faces to the ground, the men said to them, ‘Why do you seek the living One among the dead? He is not here, but He has risen.'” (Luke 24:4-5)
Notice how they are described as looking like men, not babies with wings (as is depicted in many TV shows or artworks).
Here is what some angels actually look like:
"I saw another strong angel coming down out of heaven, clothed with a cloud; and the rainbow was upon his head, and his face was like the sun, and his feet like pillars of fire; and he had in his hand a little book which was open. He placed his right foot on the sea and his left on the land; and he cried out with a loud voice, as when a lion roars; and when he had cried out, the seven peals of thunder uttered their voices." (Revelation 10:1-3)
Their might and abilities
Angels are powerful. The Bible describes them as "mighty angels" (2 Thessalonians 1:7) and "angelic majesties" (Jude 1:8). They are generally more intelligent than humans. Only in one instance are humans described as more shrewd than angels.
This was when Jesus related a parable about how a corrupt manager made friends. Jesus said:
"And his master praised the unrighteous manager because he had acted shrewdly; for the sons of this age are more shrewd in relation to their own kind than the sons of light." (Luke 16:8)
Humans are created a little lower than angels.
"What is man, that You remember him?
Or the son of man, that You are concerned about him?
You have made him for a little while lower than the angels;
You have crowned him with glory and honor..." (Hebrews 2:6-7)
Just as people are gifted with different abilities, so angels were created with varying talents they use to serve God.
Angels also learn and advance in the kingdom of heaven. Using their God-given talents, by their achievements and efforts, some angels achieve higher honors than others.
Free will
Angels have free will just like we do. When they were created, they were all good.
Some angels, however, have rebelled against God. Lucifer was the first one to rebel. And some angels followed him.
There have been several angelic rebellions since the angels' creation.
The first was Lucifer's (Satan's) fall:
"How you are fallen from heaven,
O Lucifer, son of the morning!
How you are cut down to the ground,
You who weakened the nations!
For you have said in your heart:
‘I will ascend into heaven,
I will exalt my throne above the stars of God;
I will also sit on the mount of the congregation
On the farthest sides of the north;
I will ascend above the heights of the clouds,
I will be like the Most High.’
Yet you shall be brought down to Sheol,
To the lowest depths of the Pit." (Isaiah 14:12-15 NKJV)
Another rebellion is recorded in Genesis 6:1-4, Jude 1:6-7. And there may have been more rebellions since then. The first rebellion was pride. The second rebellion was gross immorality. And other angels may have rebelled by choosing the side of evil and wanting to go their own path, instead of following God.
God's expectations of angels
It is only to humans that God gives help and forgiveness. Angels are expected to use their God-given talents and abilities to fulfill their duties.
"For assuredly He does not give help to angels, but He gives help to the descendant of Abraham." (Hebrews 2:16)
"For if God did not spare angels when they sinned, but cast them into hell and committed them to pits of darkness, reserved for judgment; and did not spare the ancient world, but preserved Noah, a preacher of righteousness, with seven others, when He brought a flood upon the world of the ungodly; and if He condemned the cities of Sodom and Gomorrah to destruction by reducing them to ashes, having made them an example to those who would live ungodly lives thereafter; and if He rescued righteous Lot, oppressed by the sensual conduct of unprincipled men (for by what he saw and heard that righteous man, while living among them, felt his righteous soul tormented day after day by their lawless deeds), then the Lord knows how to rescue the godly from temptation, and to keep the unrighteous under punishment for the day of judgment..." (2 Peter 2:4-9)
The reason God does not give angels extra help or forgiveness of sins is that angels are mighty and see God face-to-face regularly. They have no reason to sin, and they are strong enough to withstand temptations. But humans are created with flesh and blood and have weaknesses. And humans generally also do not see God face-to-face on earth.
Rank and authority
Angels have rank and authority. Some angels rank higher than others. So we have archangels, anointed guardian cherubim, and others in high places. Angels have rank also because they form the armies of God in heaven. So there are leaders of groups of angels who do battle and lead other angels into battle to fight the fallen angels.
Angels have territories they guard or watch over. There are guardian angels who guard, help, and protect each believer (Matthew 18:10). There are angels who watch over a church (Revelation 1:20). There are angels who have authority over waterways (Revelation 16:5). There are angels who guard over nations.
Michael is the angel who stands guard over the Jewish people. Michael is an archangel.
One of the angels told Daniel the prophet:
"The prince of the kingdom of Persia withstood me twenty-one days; but Michael, one of the chief princes, came to help me, so I left him there with the prince of the kingdom of Persia and came to make you understand what is to befall your people in the latter days." (Daniel 10:13-14 RSV)
So Michael is called one of the chief princes. And the prince of the kingdom of Persia is another angel, but a fallen one.
It is not because angels are compelled to be under Lucifer that no one was able to stand against the angel of the prince of Persia.
None of the angels have to follow a fallen angel.
The reason that no one was able to stand against the prince of Persia was because there were not enough people praying!
When we pray, God sends forth His angels to help us. We do battle through prayer, while angels actually fight.
This is why the Bible says: "For our struggle is not against flesh and blood, but against the rulers, against the powers, against the world forces of this darkness, against the spiritual forces of wickedness in the heavenly places." (Ephesians 6:12)
So the ruler of the kingdom of Persia were fallen angels. No one was able to withstand them except the angel who was fighting against them, and Michael, the angel over Israel.
Michael helped in fighting against the kingdom of Persia, because the Jewish people were praying for God's deliverance and to return to their homeland.
So some angels in high rank are also called princes or archangels. Unfortunately, many of the angels in high rank turned against God. So that's why there are battles everyday in the heavenly realm.
Their number
There are as many angels as there are stars in the universe. Angels are too numerous for humans to count or number.
The Bible describes heaven as having myriads of angels (Hebrews 12:22-24).
"Then I looked, and I heard the voice of many angels around the throne and the living creatures and the elders; and the number of them was myriads of myriads, and thousands of thousands..." (Revelation 5:11)
The word "myriad" means a great number that is innumerable.
"...The host of heaven cannot be counted and the sand of the sea cannot be measured” (Jeremiah 33:22)
Many times in the Bible, stars symbolize angels.
Jesus said: "As for the mystery of the seven stars which you saw in My right hand, and the seven golden lampstands: the seven stars are the angels of the seven churches, and the seven lampstands are the seven churches." (Revelation 1:20)
Even though humans are unable to calculate the exact number of stars, God “counts the number of the stars; He calls them all by name” (Psalm 147:4).
Similarly, God knows each of his angels and calls them all by name.
The elect angels
The angels who remain faithful to God are called the holy angels or the elect/chosen angels (Mark 8:38, 1 Timothy 5:21).
There are about 2/3 of the angels who will remain faithful to God to the end.
But the Bible tells us that about 1/3 of the angels rebel against God:
"Then another sign appeared in heaven: and behold, a great red dragon having seven heads and ten horns, and on his heads were seven diadems. And his tail swept away a third of the stars of heaven and threw them to the earth." (Revelation 12:3-4)
How angels help us
Angels bring God's messages, provisions (1 Kings 19:5-7), and gifts to us. They encourage and strengthen us (Acts 27:23-24). Angels protect, guard, and fight for us (2 Kings 6:15-18, Revelation 12:7-9).
They also take note of what people do, and talk to God about these things.
So that's why Jesus warns us to not treat other people badly:
"See that you do not despise one of these little ones, for I say to you that their angels in heaven continually see the face of My Father who is in heaven." (Matthew 18:10)
And Jesus also told a parable on an unforgiving servant whose deeds were reported by other servants.
"So his fellow slave fell to the ground and began to plead with him, saying, ‘Have patience with me and I will repay you.’ But he was unwilling and went and threw him in prison until he should pay back what was owed. So when his fellow slaves saw what had happened, they were deeply grieved and came and reported to their lord all that had happened." (Matthew 18:29-31)
The "fellow slaves" represent angels who report to God what we do.
Angelic judgments
Angels also have the right to pass judgement on the disobedient.
When Herod the king exalted himself like a god, not giving honor to God, an angel struck him dead immediately.
"On an appointed day Herod, having put on his royal apparel, took his seat on the rostrum and began delivering an address to them. The people kept crying out, 'The voice of a god and not of a man!' And immediately an angel of the Lord struck him because he did not give God the glory, and he was eaten by worms and died." (Acts 12:21-23)
And in the future, angels will come with Jesus to mete out punishment on the unbelieving.
"...The Lord Jesus will be revealed from heaven with His mighty angels in flaming fire, dealing out retribution to those who do not know God and to those who do not obey the gospel of our Lord Jesus." (2 Thessalonians 1:7-8)
Respecting angels but not worshiping them
As humans, it goes without saying that we should respect the holy angels. Sometimes they are in disguise:
"Do not neglect to show hospitality to strangers, for by this some have entertained angels without knowing it." (Hebrews 13:2)
We should not revile angelic majesties:
"Yet in the same way these men, also by dreaming, defile the flesh, and reject authority, and revile angelic majesties. But Michael the archangel, when he disputed with the devil and argued about the body of Moses, did not dare pronounce against him a railing judgment, but said, 'The Lord rebuke you!' But these men revile the things which they do not understand..." (Jude 1:8-10).
So not even the archangel Michael pronounced a judgment against even fallen angels, so also we who have sinned should not pronounce judgements either.
On the other hand, it is sinful to worship angels. When the apostle John accidentally mistook an angel for Jesus, the angel cried out:
"Do not do that. I am a fellow servant of yours and of your brethren the prophets and of those who heed the words of this book. Worship God." (Revelation 22:9)