My point about the victims you mentioned... even though they died tragically, it doesn't negate all the great things they experienced in life.
No, it doesn't, but if there is a creator God, then he is either a sh*tty creator or doesn't love his creation enough to give them a safe home.
Would you be fine if someone decided to crush each of your fingers with a hammer? After all, it doesn't negate the lovely dinner you had last night.
when atheists say "Why does God allow suffering" how do they define it? That is the definition I want to work towards.
Why would an atheist ask that? They don't believe in God, by definition. I think when you see that, it's a hypothetical as part of a conversation where the existence of God is assumed for the sake of conversation and there is someone, usually, a Christian, trying to say God is perfectly loving, omniscient and omnipotent.