First, our world has always been very violent because humans are violent by nature, not necessarily because we are "evil" but due to ignorance that violence of any kind whether murdering adults, children, or unborn babies, will accomplish some type of "good" - things are not any more violent now than they ever were, throughout history - it's just that now, the news services quickly, tell us about all the violence in gory details... that's the only thing that's changed.
Second, those of us who are believers should not be afraid and there is a beautiful hymn to this message (actually that was something St John Paul told us repeatedly as well).
The hymn starts like this:
"You shall cross the barren desert, but you shall not die of thirst...
You shall wander far in safety though you do not know the way...
You shall speak your words in foreign lands and all will understand...
You shall see the Face of God and live!
Be not afraid, I go before you always
Come, follow Me and I will give you rest! (taken from the Words of Jesus).
So, be not afraid... God is there by our side and He has it covered.
Why does He allow us to live in an imperfect world? To make us stronger in our Faith! So, be not afraid and remember that Jesus is right by our side and loves us, unconditionally and infinitely.