How far reaching are God's powers?

[MilesAbbott81]

And this is why you fail to be rational.  Every claim about God should be divided into two categories -- testable and non-testable. 

The non-testable ones are matters of pure belief, faith or theology.  They can have no affect on the real world, because anything non-random that affects the world can be tested.

The testable ones are really important to test.  Claims that God heals, or punishes, or does things for believers are absolutely testable.  No, the God itself isn't testable, but the claim that "if I pray for healing, it will happen more often than if I don't pray" is a testable claim.  The claim that God in any way actively makes changes to the world that disobey laws, can be tested statistically.

Now, if you are saying that God designed the laws of the universe to play out to punish people for moral failing, then I would still say this is testable.  Yes, stupidity has its own punishment, but moral failing is often rewarded by the laws of the universe unless people intervene.  Morals are not given by a god, they are part of being societal creatures.  They change according to society.  Where they have continuity, it is because of our common humanity, not because of gods.

Who says God must react on demand or obey some test that couldn't possibly be performed? How are you supposed to, for instance, measure the sincerity of someone's heart? That would be necessary to test any prayer.

The Scriptures say that our hearts are desperately wicked and unknowable, so you can't even test your own heart, much less someone else's.