LAST UPDATED 2/20 at 6:45 PM.
From what I've read, I believe Michael is more powerful, although it's always possible that Michael never faced him one-on-one. There's a mosaic at St. Peter's Basilica of a victorious Michael standing with a raised sword and his foot on the head of Satan. But that's imagery and not necessarily based on anything biblical.
Assume the chain is made by God since it has supernatural powers (otherwise, how would you chain a spiritual being?). But then, so what? The wager involves Connor choosing whom to kill using the dagger from book one. Does it matter if Lucifer is stronger than Michael or not? Strength isn't gonna decide that contest. Love might, though. De Rosa has been whispering "I love you, son" and "The world is against us" to Connor since he was an infant. Since he took Connor away from his family (his mother and her relatives), Connor had no other bonds. God only required that Connor be raised a Catholic. It was De Rosa who chose an orphanage, trying to further minimize any chance of a strong bond between Connor and others, although he develops somewhat of a bond with Romano. So, the question is, can the people who really love Connor develop a strong enough bond with him to overcome De Rosa's inertia.
Connor's Soul
Without revealing the 3rd party, I'll say that for the wager to go ahead, Satan needed an ovum and a uterus, supernaturally enhanced sperm, and a human soul. The reason it has to be a human soul is that Connor is genetically almost completely human (with DNA from his mother, DNA from the zombie known as De Rosa, and some adjustments made by Satan to the DNA in the zombie sperm to give Connor his supernatural powers). Naturally, only God can provide the soul. But why would he? Because Revelation prophecy says Christ doesn't return until after the AC appears.
Here's the catch (I think I mentioned this before): Satan asked for "a human soul." And that's exactly what he got. But Satan didn't think to insist on a "new" soul. So Connor is what we might call an "old soul". :-) But, as with Christ, who didn't know the full details of who he was and why he was on Earth until he was baptized as an adult, the soul within Connor hasn't yet fully reawakened to realize who it is, why it came, and what it's supposed to do. That soul awakens slowly over the years. In the meantime, it is heavily influenced by events in Connor's life, including the lies Connor's father told him, including Satan's manipulations to make Connor love him unconditionally. Just to be clear, that soul is Connor since Connor has no existence or will of his own without a soul. But that soul, though not fully awake and heavily influenced by current events, has instincts from it's past life, among them instincts about right and wrong, which play a role in the failed attempt to kill the pope.
So, the third party you mention, although it is Connor, isn't yet fully aware of its past. As Connor grows, his soul grows with him and changes based on Connor's experiences, since they're inextricably linked. Connor will eventually learn who he is, probably in a series of reveals, at which point he develops full awareness of true right and wrong, although there are no easy decisions (e.g., he still loves his father). But ... the soul within Connor doesn't want to burn in the Lake of Fire either (can you blame it?). So, one would think, it would be driven toward destroying Christ. That soul is, however, so traumatized by an evil it unwittingly unleashed on Earth long ago, that it planned an extraordinary rescue mission, which can only happen just before the end of Revelation. But the soul learns from God in book 2, that, for the rescue to succeed, it will need to sacrifice itself in the Lake of Fire, which it didn't expect and terrifies it. Damned if it does, damned if it doesn't. The only obvious way it can save itself is to remain allied with Satan, kill Christ, and abandon those it came to Earth to rescue.
It's at that point, when all of Connor's life experiences and relationships become critical. They will ultimately determine whether his soul has the courage to proceed with the rescue mission and sacrifice itself to an eternity of agony.
As noted, Connor is inseparable from his soul in all of this, although it becomes necessary to distinguish the two at times when writing about them. Fundamentally, there's just one soul and one body, with old experiences (from the soul's former life), which return to its awareness slowly, and new experiences (from Connor's life), which change the soul until it becomes as much Connor as not.
Inerrancy of the Bible
This is going to be complex, made more so by the need to not invalidate the Bible, which is inerrant. To understand what follows, you have to think of all of us as living in the same timeline as Connor and the wager. In other words, make believe we are on his timeline (this is fiction after all, which is supposed to take us to a universe that doesn't actually exist, so pretend it does, and we're in it). I refer to Connor's timeline as the new timeline, which began when Satan read the original prophecies, didn't like the ending, and issued his challenge to God. Our real-world timeline, where there is no Connor or wager, I refer to as the old timeline, a path we left when everything shifted to the new timeline.
Somehow (still trying to figure this out), when we shifted to the new timeline, we were left with a Bible intended for the old timeline, perhaps because a holy document originally written for one timeline won't change just because we shifted timelines. Perhaps there is only one Bible across all realities, and it cannot change, including St. John's original prophecies. So, we're on the new timeline, but our Bible was written for the old timeline. Things will happen that don't match the Bible, but the Bible remains inerrant (for its timeline).
Still with me?
Now, someone in our timeline (a saint?) in the past experienced visions (from the Holy Spirit) that our timeline doesn't match the Bible, so he wrote a new interpretation of Revelation that did match our timeline, including mention of Connor as the Antichrist and the wager. Satan got his hands on it, and made a few critical changes, one of which being that Christ will return as a boy named Connor. Satan then put it in a monastery in the 8th century, where he would later ensure that it was found. However, it wasn't taken seriously by the Church. But because the author is a saint, it also wasn't declared to be heresy. It was placed in the Vatican archives, and Cardinal Song (the False Prophet) declares it to be valid after he supposedly sees Connor (aka Jesus) in the council meeting in chapter 15. Then, as the story continues to unfold, the Council of Cardinals discovers that things are unfolding as prophesied in the ancient manuscript. Those events were inserted into the manuscript by Satan, who subsequently makes sure that the events he wrote about actually happen (e.g., Connor (Jesus) gets stabbed at the Vatican and dies, only to come back to life).
If you're able to follow that, then there is hope that I can write about it and make it work for the story. 