These questions seems to be a constant question of humanity. Why does a good and loving God allow such evil to happen? Why does God allow horrible things to happen to those who love Him? Why do bad things happen to good people? Another way to label the questions is to call it "the Problem of Evil".
The answer does not always satisfy unless you have a good idea of who God is. To really understand the answer, and in turn God Himself, then we have to dive into exploring what evil is.
First off, evil is not a thing. In fact, it is more of a lack of something else, good, than anything else. Just as darkness is a lack of light, so evil is a lack of goodness. When we think of it this way, we see that God, who is goodness by nature, did not "create" of "invent" evil. Rather, it is God's creatures' failure to be good that allowed evil to enter into existence.
Secondly, the reason that death and physical suffering exist is because there is spiritual and moral evil. The cause of suffering and death is ultimately man's sin. Because of our disobedience we suffer, in both body and soul. What we have earned by our sin is suffering and death for eternity.
This also helps us to understand the eternal love of God for us. "But God proves his love for us in that while we were still sinners Christ died for us." (Romans 5:7) Even though what we merit by our evil is death and punishment, we are forgiven.
The amazing thing about this paradox of love overcoming evil is that it leads us to the answer of why God allows evil. The answer is found in the cross.
Suffering and physical death are not good, but neither are they evil in and of themselves. In fact, through the cross, suffering and death can be redemptive. That is, they can help us to re-capture some of the purity, love and holiness that we are called to. The cross is God's answer to evil. In it, He conquers and shows us how to overcome it.
From this the questions might be turned on their head. We can now understand why bad things happen to good people, but why do good things happen to bad people? It is once again because of the love that God has for all people. Not just the "good" ones.
Suffering and death can lead to holiness and union with God. Therefore, it isn't as evil as we make it out to be. It is the eternal death of the soul we should be afraid of. All of this perfectly explains the reason St. Paul could write these words to the Romans:
"For if, by the transgression of one person, death came to reign through that one, how much more will those who receive the abundance of grace and of the gift of justification come to reign in life through the one person Jesus Christ. In conclusion, just as through one transgression condemnation came upon all, so through one righteous act acquittal and life came to all. For just as through the disobedience of one person the many were made sinners, so through the obedience of one the many will be made righteous. The law entered in so that transgression might increase but, where sin increased, grace overflowed all the more, so that, as sin reigned in death, grace also might reign through justification for eternal life through Jesus Christ our Lord." - Romans 5:17-21