If we are to love our enemies, does that mean we should love Satan?
What a great question! It is true, as you say, that we are to love our enemies. The Bible says that in Matthew 5:44 and other places. It is also true that Satan is our enemy. It says so in 1 Peter 5:8 and elsewhere. But it does not follow that we are to love Satan. Let me explain.
For one thing, the enemies that Jesus commands us to love are our fellow men. They are human beings and fellow sinners. The Bible calls us to love our enemies because we are just as human, sinful, and prone to failure as they are. Satan, on the other hand, is a fallen angel. Nowhere does Scripture call us to love angels. Instead, the Bible teaches that angels were created for two main purposes: to worship God (Hebrews 1:6) and serve God's people (Hebrews 1:14). Satan failed on both counts. He is under the eternal wrath and curse of God, without hope of mercy. He is not to be loved by believers, but resisted and abhorred.
For another thing, consider Psalm 139:21-22, which says, "Do I not hate those who hate you, O Lord, and abhor those who rise up against you? I have nothing but hatred for them; I count them my enemies." These verses may surprise many Christians. Some think that we are called to be "nice" to everybody, never to judge or criticize. The fact is that love sometimes includes judgment. (For an example, see 1 Timothy 1:18-20.) If this is true in our dealings with human enemies, how much more it should be true in our dealings with Satan! I suppose you could say that the most "loving" thing we can do toward Satan is hate him, call God's judgments down upon him, and eagerly await the day when he will be thrown, with all his demons, into the lake of fire (Revelation 20:10).