Well I think that the two kinds of "evil" that you describe are just completely unrelated.
We know how hurricanes form, and we know why earthquakes happen and we know (or learn) how deadly diseases spread. The victims are not victims of evil. They were just at the wrong place at the wrong time.
Accidents? The kid who fell down the well, the tween who swam was on a beach vacation with her family for the 4th of July who got swept out to sea and died, the family in the SUV who got sideswiped by a sleep deprived truck driver and all perished, these are harder to accept. We all wish we had DONE SOMETHING to prevent the events. We relive the events in our minds, and rehearse changing one little thing, and erasing the event from history. But we can't.
Human "evil?" Well. There is certainly mental illness. Those who have no respect for the value of life, or those who derive joy from causing pain in others. There is greed. (Waving at Junebug). There is ambivalence. Sometimes I think that is the worst. The bankers who focus on the bottom line rather than the families who are losing their homes. The consumers who are vaguely aware of the fact that child labor is responsible for many of the items in their home, but who convince themselves that the children who are putting in 14 hour days in garment factories are not like OUR children. And then there are the damaged people, whose pain is so huge that they don't even realize that causing pain in others is not the way thing should be. The solution? For just about everything but the most serious mental illness is empathy. We need to really put ourselves in the position of others to understand that harm that we cause. And we all cause harm.
Sometimes "evil" is subjective. There are "evils" committed by one faction against another faction. . That "evil" clan is stealing our water and our hunting grounds and if they keep doing it the people I love are going to die, so I have no choice but to kill them. And the survivors of the massacre can attest to the evil committed by the murderers. The loved ones of the Iraqis who died when the US went in to liberate them find little comfort in ideology that brought the foreign troops.
Again, the solution, in my humble opinion, is empathy. Not religion. Not a god who is going to make everything ok. Just empathy.
Oh! And welcome to the forums. We look forward to hearing more about your beliefs and life experiences and sharing banter with you.