1. The discovery of a naked singularity –a point in space which could literally spew forth anything “out of the blue” –chairs, pizzas, computers, works of literature, or whatever.Now let's say we found a singularity that spewed forth chairs and pizza. Mr. Torley could easily say "Ah, but it is not spitting out computers and works of literature. Or leprechauns and unobtainium." It's a bit like trying to prove that all swans are white. Plus, I don't understand why such a finding would be detrimental to religious faith in general.
To the point, several of his challenges have to do with the brain and behavior. Whatsmore, many of these have already come to fruition and therefore he should reject his faith.
5. The invention of a machine that could control the propositional content of my thoughts, and make me believe anything that the machine’s programmer wanted me to believe –or do the same to any other human being who is currently capable of exercising their faculty of reason.Has Mr. Torley never heard of deep brain stimulation? It has been used extensively in Parkinson's patients and has the (not unexpected) outcome of sometimes increasing risk taking behaviors. Use of DBS has been expanded in recently for therapeutic use in addictive behaviors, depression, and OCD. These last three all involve altering how the patients thinks about the world, i.e. they alter the propositional content of the mind. (I know he limited this to machines, but I think we can assume that Mr. Torley has never experimented with recreational drugs or else he would not have issued this particular challenge.)
6. The invention of a machine that could control my actions, without impairing my ability to reason and without impairing the link between my beliefs/thoughts/judgments and my actions –or do the same to any other human being who is currently capable of exercising their faculty of reason.Well, we are quite capable of controlling the movements of rodents by stimulation of the medial forebrain bundle, and the only reason we don't do so for otherwise normal humans is because of ethical limitations. Even if Mr. Torley is offering to volunteer, I think he would be hard pressed to find a scientist willing to hook him up.
7. The invention of a machine that could turn me into a person who would willingly perpetrate atrocities like those those committed by the Nazis, without impairing my ability to reason and without impairing the link between my beliefs/thoughts/judgments and my actions –or do the same to any other human being who is currently capable of exercising their faculty of reason.Sweet Jeebus, didn't this guy ever come across Stanley Milgrim in his studies? What's amazingly scary is that it is incredibly easy to get people to go along with committing atrocities if you command authority. If we just replace Milgrim with a computerized sexy voice we've got an instant mechanized Nazi maker.
So, Mr. Torley's faith should be crumbling all around him. More likely though he is busy propping up his faith walls with nitpicking and elaborations on what he really meant. There is advantage to being vague in your statements.