I do not know of any specific incidents in the Bible where the devil answered prayer. The closest I can think of is in the temptation of Jesus. After the devil had shown Jesus all the kingdoms of the world, he said, "All these things will I give thee, if thou wilt fall down and worship me" (Matthew 4:9). That is pretty close to prayer and a promised answer, just not exactly.
However, we do know that the devil has much power and it would seem that some of that power could be displayed in giving to his followers some of the things they ask for. When the archangel, Michael, fought with the devil over the body of Moses, he said, "The Lord rebuke thee" (Jude 1:9), indicating that Michael's power alone was not enough to overcome the devil's power. The future coming of the Antichrist will be "after the working of Satan with all power and signs and lying wonders" (2Thessalonians 2:9). Revelation 13:11-15 says much of this power of the devil. The false prophet will heal the deadly wound of the Antichrist (v.12). He "doeth great wonders, so that he maketh fire come down from heaven on the earth in the sight of men" (Revelation 13:13). He will deceive the inhabitants of the earth "by the means of those miracles which he had power to do in the sight of the beast" (v.14) and he will give life to the image of the beast (v.15).
We certainly should not pray to the devil. However, in a limited way, the devil probably has the power to answer prayer on some occasions. However, we should never think that his powers in any way come close to the power of Almighty God.
