Hi Richard, I hope you don't mind if I separate your first question from the other two. The Russian writer Dostoevsky prophetically explored this question in his last great book, The Brothers Karamazov, where Ivan Karamazov depicts Christ, once again being judged, this time by 'The Grand Inquisitor,' for the crime of overestimating human beings by granting them freedom - a freedom which Ivan shows has led to horrible crimes. Before sentencing Christ to death, Christ is told by the Inquisitor that 'we have corrected your work' - by taking away human freedom. One of the best Russian Dostoevsky commentators notes that behind Ivan's 'false compassion for the sufferings of mankind is hidden a diabolic hatred of human freedom and the image of God in man.'
The mystery here is that if God creates beings endowed with freedom, they must be able to choose good and evil, where that evil will sometimes include the slaughter of millions of innocent human beings you mention. In a little book I wrote last year, Where Is God In Suffering? I gave the example of married couples who have the choice to bring a child into the world, without being able to determine whether their child will turn out well or badly. Yet they take that risk - as God does when he created angels, and when, through our parents, he co-creates us. God's own answer to your question is to come right down into our world, and experience evil head on in his incarnate humanity. The Crucifixion, Death and Resurrection of Jesus is - for whoever want to follow him - the way of the Christian to overcome evil with self-sacrificing love united to Jesus' own self-sacrificing love.
In that little book, I mention the Dutch Jewish woman, Etty Hillesum, whose letters and diaries indicate someone who herself grew under the imminent threat of her extinction - she was killed in Auschwitz in 1943. Because of her position in the Jewish Council she could have escaped the concentration camp where she worked to help the Jewish inmates, but chose to remain with them, writing in her diary: 'And if God Himself should feel that I still have a great deal to do, well then, I shall do it after I have suffered what all the others have to suffer. And whether or not I am a valuable human being will become clear only from my behavior in more arduous circumstances. And if I should not survive, how I die will show me who I really am.' While not a Christian, she understood clearly that her freedom was something the Nazis could never take away from her, and her writings show how in fact she grew enormously through what she called 'the art of suffering.'
Asked by a young man in Nairobi in November 2015 a question very like yours, Pope Francis repeated the question: "'How can I see the hand of God in one of life's tragedies?' I was going to say there's just one response but no, there's no response. There is a path." In other words, the only 'answer' is how we ourselves endure the suffering that comes our way - do we take up Christ's advice and carry our cross every day, or do we refuse to? Let's have a look at your other two questions, which might help us on our way.
The question about world hunger is maybe the easier one - I can't think of a single case at present that isn't closely tied up with poor or corrupt human governance. The worst famine in modern times, in China from 1958 to 1962 when up to 45 million died, was directly due to Mao's catastrophic mismanagement, the Russian famine of 1921 resulted in 5 million dead, and in Ukraine, 1932, in 6 million deaths - the first was Lenin's choice, the second, Stalin's. The 1983-85 famine under Mengistu in Ethiopia led to nearly half a million deaths. All of these famines were 'planned' in that they were a direct result of ideology-driven government policies.
The Irish famine of 1846-47 and its aftermath left a million dead, a million forced to emigrate, was due to poor Irish farming practices (depending on just one crop, potatoes), the Irish inheritance structure that meant subdividing farms into smaller and smaller units, unable to support even one family. Along with these causes was an uncaring British government policy that regarded the native Irish as somehow less than human. God gives us humans reason and the ability to solve these problems - in fact, countries where famine was endemic, especially India and China, are supporting far greater populations than ever, once they sorted out their agricultural policies.
Regarding the suffering or affliction with disability of young children, there's no answer other than the love and care such suffering evokes - which may be the nearest to an answer that we can get in this life. While he wasn't a child when he said it, I've never forgotten what Eddie McCaffrey, a friend of mine suffering from muscular dystrophy (a genetic illness that left him without use of his legs or arms), said about someone he know who suffered from depression. 'It's a pity he doesn't understand, you don't solve problems, you love them.' That had been his own experience - he didn't want a miraculous cure, just whatever God wanted for him. His loving, or fully accepting, that had meant he somehow managed to leave his 'problem' behind. He lived his suffering so well to his death at 31 years old, that many young people from Northern Ireland and the Republic found their way to God through Eddie.
These are just pointers, it's only by trying ourselves to live our sufferings - united, if we're Christians, to the God who shared them in his Son, Jesus - that we'll glimpse a kind of answer there. Very best, Fr Brendan