How do Christians explain the cruelty that seems so common place in our world? I'm not only referring to that inflicted by humans, but also to that in nature.
It is a world where everyone (everything) is obsessed with their carnal needs and desires. Whereas a world of godly people produces peace and love, because we do not care only for our selves, but we care for each other. The prophet Isaiah has expressed the vision that God showed him, of the way He wants the world to be:
In that day the wolf and the lamb will live together;
the leopard will lie down with the baby goat.
The calf and the yearling will be safe with the lion,
and a little child will lead them all.
The cow will graze near the bear.
The cub and the calf will lie down together.
The lion will eat hay like a cow.
The baby will play safely near the hole of a cobra.
Yes, a little child will put its hand in a nest of deadly snakes without harm.
Nothing will hurt or destroy in all my holy mountain,
for as the waters fill the sea,
so the earth will be filled with people who know the Lord.
I believe this was God's vision from the very beginning, when He blessed the man and woman and instructed them: fill the earth and subdue it.
Why are there diseases that cause such huge suffering?
Too much wasted human resource (eg war, poverty), causing critical delays in human technological and medical advancement.
Why is it necessary for animals to live by eating others, in some cases whilst still alive?
Is it a fact that it is necessary rather than normal? Please show me some examples that you have in mind. I know it is possible to feed cats and dogs a vegan diet, for example, so do you think it is reasonable to believe that all creatures can survive on vegan diets if they can become accustomed to it?
Why have natural disasters that cause death, pain and suffering?
All 'natural disasters' are simply an inability to cope with natural conditions. Sometimes those natural conditions are made worse by human actions (eg a rise in atmospheric CO2 levels causes greater velocity of cyclonic action). Other times it is due to humans not exercising the right amount of caution (eg, the building that collapses in an earthquake could have been made more robust).