Please enlighten us then.
You can't scientifically examine a claim. If there were something to examine, it would be more than a claim.
No. Pretty much everything in psychology is rigorously scientifically examined. Maybe you are thinking of other types of social sciences. Gender studies?
Probably not. The only thing both sides can agree on is that there are recorded instances of strange objects that are unexplained. Where they disagree is whether the objects are natural, human made, or involve some other causes we do not understand.
I said psychiatry not psychology and I stand by what I said about psychiatry not strictly being able to apply the scientific method successfully. Not everyone responds the same as others each time which negates the application of scientific method. This is one of the reasons that psychiatry is recently undergoing scientific re-examination. More conditions that were categorized as psychiatric are being shown to be medically caused (by infections in the brain, for instance).
If someone "claims" that they can move objects with their mind power, why can't that be tested? Show me that you can do this under conditions that I can scientifically set as tests.