No, the devil hasn't always existed. Only God is eternal and has always existed, and only He had the power to create everything that does exist - including us. "For by him all things were created: things in heaven and on earth, visible and invisible... all things were created by him and for him" (Colossians 1:16).
The Bible doesn't answer all our questions about the devil - but it does tell us that before time began God created a great multitude of angels. Satan was one of them, and was apparently given a place of high authority. The angels were created to serve God and obey His commands, and as an angel, Satan also served God. But Satan rebelled against God, persuading other angels to follow him in a massive cosmic rebellion against God's authority.
Why did he rebel? The answer can be given in one word: pride. He became jealous of God, and in his pride he wanted God's glory for himself. He declared, "I will ascend to heaven.... I will make myself like the Most High" (Isaiah 14:13-14). His rebellion failed - but Satan's goal is still to stop God's work.
The most important fact about Satan, however, is this: Satan is a defeated foe. By His death and resurrection Jesus overcame Satan's power over us - the power of death and Hell and evil. Is your hope in Christ, both for today and for all eternity?