"Is there more than one 'Satan?'" Yes there is, and why...
The term Satan, like President, just means Leader [of Opposition], often rendered Accuser or Opponent. Jesus even called Peter (His Rock) a Satan once here:
“Get behind me, Satan...you are not mindful of the things of God, but the things of men”.
Please never believe that any Satan ever works for God, the Lord outed all Satans mindsets as being ungodly [always]. The Satan of Matthew 12:26 NKJV is a hypothetical one because you cannot have two Satans in the same rebellion. The Jews where accusing Jesus of being a Satan working for Lucifer.
If Satan casts out Satan, he is divided against himself. How then will his kingdom stand?
The Book of Revelation says Abbaddon is a leader of a separate kingdom of evil spirits (Locusts, neither Scorpion or Serpent) who is locked in the Abyss; Lucifer is in Hades - totally different places.
The locusts had a king over them--the angel of the bottomless pit, whose name in Hebrew is `Abaddon,'
The Book of Enoch explains his name as Shemjaza the Chairman of the 200 dissenters in the separate rebellion from Lucifer's. Nothing in the Bible nor Enoch proves that these 200 dissenters were part of Lucifer's rebellion.
To further complicate matters Lucifer deploys diametrical opposition to counteract the Kingdom of God. So if God is a Holy Trinity, Lucifer wants to be an Unholy Trinity:
1.Satan the Opponent = Who is in Hades.
2.Satan the Accuser - Who is in the Lower Heaven.
3.Satan the Antichrist = Who rules on Earth.
The name of the first and last Antichrist spirit is Nimrod, I cannot pin down the identity of The Accuser just yet. So..
1.Lucifer Opponent Satan.
2.Nimrod Antichrist Satan. And
3.Abbaddon-Appolyon-Shemjazza Satan are three of four 'Satans' known to us today. But 3.Abbaddon-Appolyon-Shemjazza is not the same faction as Lucifer. As for your last question I can never accept that any of them work for God.