Answer: At first it might seem that if God created all things then evil must have been created by God. However, there is an assumption here that needs to be cleared up. Evil is not a "thing" - like a rock or electricity. You can't have a jar of evil! Rather, evil is something that occurs, like running. Evil has no existence of its own - it is really a lack in a good thing. For example, holes are real but they only exist in something else. We call the absence of dirt a hole - but it cannot be separated from the dirt. So when God created, it is true that all that existed was good. One of the good things that God made was creatures who had the freedom to choose good. In order to have a real choice, God had to allow there to be something besides good to choose. So God allowed these free angels and humans to choose good or non-good (evil). When a bad relationship exists between two good things we call that evil, but it does not become a "thing" that required God to create it.
Perhaps a further illustration will help. If I were to ask the average person "does cold exist?" - his/her answer would likely be yes. However, this is incorrect. Cold does not exist. Cold is the absence of heat. Similarly, darkness does not exist. Darkness is the absence of light. Similarly, evil is the absence of good, or better, evil is the absence of God. God did not have to create evil, but rather only allow for the absence of good.
Look at the example of Job in Job chapters 1-2. Satan wanted to destroy Job, and God allowed Satan to do everything but kill Job. God allowed this to happen to prove to Satan that Job was righteous because he loved God, not because God had blessed him so richly. God is sovereign and ultimately in control of everything that happens. Satan cannot do anything unless he has God's "permission." God did not create evil, but He allows evil. If God had not allowed for the possibility of evil, both mankind and angels would be serving God out of obligation, not choice. He did not want robots that simply did what He wanted them to do because of their "programming." God allowed for the possibility of evil so that we could genuinely have a free will and choose whether we wanted to serve Him or not.
Ultimately, there is not an answer to these questions that we can fully comprehend. We, as finite human beings, can never fully understand an infinite God (Romans 11:33-34). Sometimes we think we understand why God is doing something, only to find out later that it was for a different purpose than we originally thought. God looks at things from an eternal perspective. We look at things from an earthly perspective. Why did God put man on earth knowing that Adam and Eve would sin and therefore bring evil, death, and suffering on all mankind? Why didnt He just create us all and leave us in Heaven where we would be perfect and without suffering? The best answer I can come up with is this: God didnt want a race of robots who did not have a free will. God had to allow the possibility of evil for us to have a true choice of whether to worship God or not. If we never had to suffer and experience evil, would we truly know how wonderful heaven is? God did not create evil, but He allowed it. If He hadnt allowed evil, we would be worshipping Him out of obligation, not by a choice of our own free will.