How many soldiers on both sides were arrested for war crimes and how many were convicted and sentenced?
Is the definition of a war crime during the ACW any different from what is defined as a war crime today?
This is going from memory, but I believe that the United States tried about seven hundred Confederates-not all of them soldiers by any means-for purported violations of the laws and customs of war. Of these, in the vicinity of two hundred were executed. A comprehensive list of these executions does not exist. The vast majority of these cases occurred prior to the surrender at Appomattox. They typically involved alleged spying, partisan activities, murder, arson, bridge-burning and the like. Most of these cases were tried by military commission but a number of extra-judicial killings also occurred.
After the war, excluding the four Lincoln assassination suspects, only three Confederates were executed for war crimes. Most Confederates sentenced to imprisonment for violation of the laws of war were simply released at the end of the war. An exception was Sam Berry who ended up serving seven years at Albany Penitentiary in New York before dying in 1873.
A number of Union soldiers were executed by Confederate military authorities on various pretexts, but the exact number escapes me, and again no accurate list (if any at all) exists that I am aware of. Some of these, like the Andrews raiders, would have been executed on charges of spying, which is a violation of the laws of war. I exclude from this any cases of Union personnel executed or killed on charges of leading or inciting servile insurrection because they led USCT. The Union side, certainly, would not have conceded this to be a crime (and I sure don't either).
As for your last question, I really wouldn't want to speculate because my knowledge of American war crimes trials basically stops after 1951, and I am not a lawyer. As long as we are talking about alleged violations on or in the vicinity of the battlefield, then I would say the treatment of war crimes on a procedural basis up until 1951 is substantially similar (and indeed rooted in) to the treatment of war crimes in the Civil War by American authorities. Beyond that, I have no real idea.