Generally its agreed that science is any theory that makes a testable prediction. Some will argue, for example, that 'astrology is not a science'. I disagree. It IS a science in the sense that it makes a testable prediction: that significant events (deaths of close family members, birth of children, etc) in a person's life is correlated to the position of planets in the various constellations.
Some people claim that 'intelligent design' is not a testable theory. I disagree. It is testable just as a claim on the origins of the great pyramid is testable.
So Dawkins is right when he says that the claim that 'God made the universe' is quite possibly a testable claim. This is what allows him to claim that it has been falsified.
This would, however, depend on the specific theory. For example, the 'theories' of intelligent design creationism so far are untestable. Perhaps 'discernable' is a better word here. For example, Behe's irreducible complexity concept has no way to discern his theory from 'not knowing' something and therefore fails as science.
I would agree that we could make tests for intelligent design. Based on our knowledge of human design and genetic algorithms, for example, we could say that if we encounter something that falls in a twin-nested hierarchy, it is probably not designed. For my part, I do consider intelligent design falsified for this reason.
Not Christians, but religious people across the board have been shown quite consistently to be 'happier' than atheist/agnostic counterparts in several studies.
More than 70% of randomized double-blind studies indicate a positive correlation between prayer and health. Of course, we can debate about whether 'God' is involved. Nevertheless, the positive benefits of prayer are well documented.
Citations? My suspicion would be that this would be due to community binding. For example, it has also been shown that people with a conservative background put more emphasis on community than people with a liberal background and are on average more at ease with others and more likely to seek the company of others. But due to the linkage between fundamentalism and conservatism, religious studies would show the same effects. So you'd have to control for factors like community cohesion. Did these studies do that?
Same with prayer. Meditation has also been shown to have health benefits and prayer can be seen as a form of meditation. Is the meditative part responsible for the benefits or the 'god'-part? Has this been tested? How does meditation compare to prayer as far as health benefits go?
Neither can science examine consciousness in any meaningful way because it is difficult to define. Yet I am absolutely certain it exists.
Science can still investigate something when it is vaguely defined. Making testable hypothesis can than lead to better, stricter definitions. Science can that way at least put a boundary on the problem. As it does with consciousness. This makes consciousness a problem that can be investigated.
For God, we can this way at least deliminate the problem. Point is that with God, other than with consciousness, this delimination has lead to the rejection of virtually all clear definitions. This means that the only thing left is something so badly defined that it cannot be tested anymore. That makes it unscientific (or perhaps 'beyond science', as people like McGrath would like us to believe).