Then they have skewered definitions of the term.
If you're in a country that's at war with another, the entire country is at war. Not just the soldiers, not just the government, it's the ENTIRE country. The civilians are a part of it and they all form the infrastructure that helps power the military machine. It doesn't matter if you don't agree with the war, if you still consider yourself apart of the country and you don't leave it, you still add to its overall mass. These governments represent us; if one disagrees that, they need to leave.
The 9/11 attack was carried out by a group of individuals who are simply well sponsored by outside elements that could have declared war but instead decided to hide behind the Osama figure-head. They are terrorists, not soldiers.
Aside from your semantics in terms of definition, what do you consider the difference between soldiers and militarily-trained terrorists?
As for the bomb, people always look at is a yes/no type of decision. Why no "warning shot?" We could've dropped it onto a more remote region where the destructive power could be seen without killing many (even a small military post). The Japanese were already considering a surrender before we dropped the bomb, just showing the power of it without killing all those people would've had the same effect.