The question posed had mutliple parts.  The first part was, "If God is powerful enough to stop injustices then why doesn't He?"

I'm an atheist but I understand that free will requires the ability to do both good and bad.  If God were to stop anyone of us from doing evil then He not only prevents the expression of free will on the part of the evil doer but also prevents the chance for the rest of us to express our free will.

An Example of the Free Will Argument

Let's imagine a particularly horrible crime where an adult intends to rape a child.  We all want this prevented. 

Let's consider the crime.  An adult, probably a man, wishes to rape, abuse and then murder a child he is already in possession of.  If God were to precent the evil from happening then God has not only prevented the expression of this man's free will but He has also prevented the evil man from chaning his mind at the last second.  God has also prevented the man from learning to not be evil.

For the rest of us, had God prevented the crime He would also be preventing us from expressing our free will in our response to the evil.  A community drawn together is search for the child.  People from different idealogies brought together to find the perpetrator.  And finally the lessons learned about human nature during the discussions on what constitutes a just punishment.

To prevent injustice is to prevent man from fully understanding human nature and it completely prevents us from understanding justice. Some may argue that God could allow us to experience small injustices so that we may learn justice with a small price tag. I disagree.

Another Example: Hitler and the Holocaust

Hitler killed millions of Jews in a particularly heinous and cruel fashion. If you could travel back in time would you?

My answer to this is NO. Not because I want to see millions tortured and executed. Not because I am callous or a bigot. But rather because I believe Hitler was an expression of the times. In other words, if it hadn't been Hitler it would have been someone else later on and maybe Hitler was the least bad.

If Hitler had been less manic... If Hitler had listened to men such as Rommel... If Hitler had waited another year to attack Russia... The world would be a much different place than it is today. Millions of Jews had to die for mankind to discover and agree on the concept of a crime against humanity. Today we declare much lesser offenses than Hitler's to be crimes against humanity and we hunt the perpetrators down.

Additionally, Europe and the US became much stronger friends. The global economy that we've enjoyed for the last 50 years is a direct result (good or bad) of WWII. Not only have we learned how to kill each other better because of WWII but we also apply those technologies to medicine and energy production.

Maybe God's kindness is in letting us learn those lessons with Hitler instead of someone more devious, more cruel, and more disciplined.

We cannot understand hot without cold, dark without light, or justice without injustice.

To deprive man of an understanding of justice would be a crime.  So we must experience injustice in little ways and major ways so that we may understand justice in all its forms.