I'll list some thoughts I have on some of Kyon's assumptions...

"Is God willing to prevent evil, but not able? Then she is not omnipotent."

It bugs me that "evil" is spoken of as an absolute concept that apparently everybody knows about; an omnipotent god simply may have a different concept of "evil".

And of course gods that encounter problems are not omnipotent, or they'd just remove them with a thought.

"Is God able, but not willing? Then she is malevolent."

There may be good reasons why "preventing evil" would do more harm than good, reasons we can't or don't want to see. (This is why people have faith in something, be it gods, politicans, doctors, their fellow citizens, and so on. Faith is just the assumption that things will turn out to be OK if certain rules are followed.)

"Is she both able and willing? Then whence evil?"

Again, a god may have a different concept of "evil".

"this world where children go hungry and die, where children get sick and die, where children are abused and even sold into slavery, where a hundred and fifty thousand people die every day - this world can't be forgiven, Haruhi. If someone deliberately made this world like that, then she couldn't be forgiven either"

Children need space and food; humans (like all species) tend to produce more offspring than the world can sustain. Does that condemn a world? Is death a flaw, or isn't it rather the natural way things are supposed to happen? Creatures always try to survive, but modern man might do more harm than good in blindly following that instinct.

Of course a god might still decide to prevent injustice, like a comic book action hero.