Do Christians believe that the devil's power is equal to that of God?

No, Lucifer was an angel. Angel's are below god.

No! The Devil is only an Angel...true he was probably the third Arc-angle, but an angle never the less.

He has only power an angel would have, and he can only use that power when approved be God.

I'm a Christian and I have never believed that there is an actual devil. It is a myth as far as I am concerned

No. The devil is not a god, or God's rival. He is no way any equal to God.

no , Satan is a created being (by God) and in no way has equal power

Satan is the 'god' of this earth. We believe that the Holy Spirit is preventing Satan from running wild on planet earth.

Until a later time when the Holy Spirit leaves this earth.

They also believe that satan IS the god of this world, go figure that one out.

Revelation 1:18 I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death.

Absolutely not.

No, of course not.