Question: Why exactly did the Devil keep Jericho alive? Why didn't he just have his followers kill him while they were tying him up?
Answer: It's not explained why he didn't kill him then. Any answer is speculative, but the obvious one is that Jericho is the main protagonist in the story and the plot needs to be allowed to play out in a contrived way to provide a satisfying conclusion. Abruptly killing off the character would end the story.
Question: How was Thomas Aquianes able to track down Christine in New York city? He was never told where she was born and for all he knew, she could've been born anywhere?
Answer: The Vatican is aware of the birth, somewhere in the world, of Christine (though not knowing her identity at the time), and the Satanists are present at her birth and know that she is "the one." It's safe to assume that the Vatican, and the Catholic Church in general, has spies/informants in the Satanists' society, and were able, in the intervening 20 years between Christine's birth and the events of the film, to track her down to New York and send Aquinas there (the fact that he was sent by the Vatican is established).
Question: Why wasn't Christine ever told by the devil worshipers who raised her that she was the devil's wife?
Answer: She wasn't exactly fond of the fact when she learned the truth. Telling her before then could ruin Satan's plan, i.e. the revelation could cause her to commit suicide years before the ordained time or she could flee to where they may never find her.
Question: Why does Satan go through the trouble of hiring protective detail at the beginning of the film? Bullets have no effect on him, and even if he was hit, he could just make the claim that the shooter missed. And it's not like he's overly worried about people discovering his true identity, since he blackmails and corrupts people throughout the movie.
Answer: It is never explained and is considered by many to be a major flaw in the film. Presumably Satan wanted to torture Jericho, he definitely seemed to enjoy tormenting him throughout the film.
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