How Do Demons Exist and How Do They Multiply?

The first fact to be noted is that nothing exists if God does not cause it to exist. The existence of all things depends on God.

God, who made the world and everything in it, since He is Lord of heaven and earth, does not dwell in temples made with hands. - Acts 17:24 (NKJV)

The earth is the LORD’s, and everything in it. The world and all its people belong to him. - Psalm 24:1 (NLT)

Another notable point is that when the devil was created, he was not known as Satan (which means adversary, opponent, enemy…). Initially, he was an angel – A Cherub

12 “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!
13 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;
14 I will ascend above the heights of the clouds, I will be like the Most High.’Isaiah 14:12-14 (NKJV)

He became Satan because he ambitioned to become equal with God himself. This got him sent out of heaven.

Demons likewise were not created to be evil beings. The became demons because they decided to be on the side of the devil when he was sent off from heaven.

And angels who did not keep their own designated place of power, but abandoned their proper dwelling place, [these] He has kept in eternal chains under [the thick gloom of utter] darkness for the judgment of the great day, - Jude 1:6 (AMP)

Angels/demons do not procreate or multiply like humans and other living creatures.

For they are spirits of demons, performing signs, which go out to the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty.Revelations 16:14 (NKJV)