I have not worked on Phantom, but I know / have worked with many who have.
I am going from recollection, so please forgive me.
Re: Christine alternates: As I recall being told, there was significant debate from AEA about a Christina alternate since Brightman was coming over for the UK and ensuring that the alternate role would be for an American actress as a condition of Brightman's employment. Once a show is open, you can NOT reduce the number of AEA contracts on the show (Unless you halt performances / close long enough to negate contracts)... Hypothetically, they could turn the Christina alternate track into a stand-by track or a swing track, but once something is set, you often don't want to.
Re: Pre-recorded vocals and off-stage vocals: Yes, the recorded tracks are individual and are set as part of the show's pre-set, and there absolutely have been times where the wrong performer's track has been played. With doubles, racing to places backstage, and yes, VERY loud stage mechanics on Phantom, singing live off-stage is not always possible because the sound will be compromised. Can some Christine's hit the Money Note 6-8x a week? ABSOLUTELY, but again, *that* changes the job for a lot of other people during a performance, so you don't. You do that show as set.
Re: The Red Death costume: It is physically impossible to sing in that costume, and the actor has VERY limited vision and their ability to hear is somewhat compromised as well. Even IF the actor could sing in that costume, it would be near impossible to mic cleanly.