No, it is excluded by the definition, with science defined as the study of the physical/natural - supernatural possibilities are excluded by definition.
No. Science is methodologically naturalistic. That means that science can only use observations from nature to understand things. The method came long before anyone used that definition. Magic, prayer, and revelation are beyond science, which has no way to evaluate any of that. The most science can do, is to say whether or not there is a natural explanation for things.
It cannot serve it's purpose to research the physical and natural worlds unless it excludes all else, that does not mean that there is no objective way to test the supernatural.
For a Christian, God is responsible for supernatural things, just as He is responsible for nature. It's blasphemous to test God.
That is exactly what all established spiritual/religious systems are in my opinion. That is what they are intended for - they are applied philosophies. I do not buy the myth that they are failed prehistoric attempts at science
I've heard that from creationists, but it's wrong. There was belief and superstition, and magical thinking long before anyone figured out science.
There is a God regardless of how we feel about that as individuals -
But since there is no consensus by believers on even very basic things about God, it would seem that religion is not a very reliable way. Hence, the Bible and general revelation. But even that is not enough to produce a consensus. And I think I know why. God seems to find it very important that each of us come to Him willingly. And if He made Himself demonstrably true, who would have the freedom to decide?
Maths is not subjective, it also is not physical - it is theoretical
So is plate tectonics, gravity, evolution, atoms, etc.
but 5 + 5 = 10 even if it feels like it should be 24 to someone.
But 1+1= 10 sometimes, even if it feels like it should be 2 to someone.