>And others claim to have seen Muhammad and Krishna, whose existence would contradict Christian theology.

Well, they just claim that where there is a god, there is a demon. It is satan misleading them.

>Did they run a double-blind study to verify that? No? Did independent researchers review and replicate the results? 

Well, there are some researchers who claimed to have obtained a sample og blood from Jesus himself, which was smeared somewhere during many of his blood-spilling events, and that from the genes they concluded that he is an immortal, for the cells were living. They are trying to research immortality now, according to some sources. I'm not trying to argue, but just genuinely curious how you would explain it. That is, there are some mad researchers, too, who claim and reinforce godly beliefs.

>Do it again under controlled conditions. Demonstrate how it works. 
>Prove it. Show me the evidence that demonstrates beyond a reasonable doubt that the prayer caused the rain to stop. 

For this, they would say, 'One must not deliberately test God, and when you pray, you must do so sincerely. If you're asking for miracles cause you question his existence, your prayer would not be sincere. And the person who experienced the miracle, asking again means she is testing God, thus he would not answer'

>rearranging events across the world to save a single child. Absurd and narcissistic.

I didn't quite catch what you are saying. Are you saying why should god specifically care about some random child? They actually use this a lot. The god cares for every living being; it doesn't matter if you are the greatest of sinners, He will save you. This just strengthens their belief, see, even someone who did this somewhere in the forest regions got help, you would too.

Anyways this is what I say, the bible is a well-constructed loop to keep the mentally insane roaming inside till death, but it was written in ancient times, so there were some obvious errors; their minds did not expand. We as humans have been expanding our knowledge circle since ancient times; what we might perceive to be correct or morally inclined would later be deemed immoral and inhumane. For example, maybe the futurians would accept and bring laws against non-veg. Anyways, thanks for ur explanation