You are asking how evil can exist in a world where God exists. It can't exist in a world where He doesn't.
Ultimately, should He exist, the world is founded to His demands. Should it not, it is structured to no one's. Thus, your concept of evil is just a concept. You see, for this to be a world of consequence, there must be ultimate consequence. For instance, you may want not want to die. There may be someone who does. Death, without consequence, is ultimately not a bad thing. And ultimately then, death being the fate of all living things, evil cannot befall the living.
And your argument of evil is thus that it is evil if God exists, but is not if God doesn't. You may not have argued that, but your argument can be reduced to it.
And evil can also be used to prove God, as you obviously know that there are some things that are evil. Matter moves according to how it is pushed and pulled, attracted and repelled. Animals move to such principles, and to their desires, and to their survival. Humans, too, would be expected to move to their interests. Humans are the only known living creatures, however, that condemn such things. If you are robbed, you feel yourself wronged. If you had a close friend or relative murdered, you feel grieved. (At that point also, you must note that justice and revenge are human concepts that only rule over humans.)
Regarding the things of angels and men: angels and men are both under consequence. Such is included in the clause of free will. Angels were created conscious; they don't spawn (or, they aren't supposed to: The Sons of God are an exception by their own devices); they don't have blood. All of these things are rather important. Men are born, and born ignorant. Thus, salvation comes by birthright because salvation is in human blood. Being born ignorant makes irrelevant the folly of Adam. It is not the sin of Adam that lies upon the hearts of man, but the sin of man. Those who die in ignorance, meanwhile, get judged to different standards. There is the concept of the age of accountability, and there is the concept of those dying who've never heard the gospel. Accordingly, they get judged to their own righteousness. This is relevant because you've declared that there is evil in the world; how could you know such a thing? Regardless, those that violate their own conscience have violated the laws of God. It is not even the sin of Adam that will determine their fate.
However, your concept of God, while low to my standards, is actually quite high to God's standards. You see, your potential for knowledge is unmatched. Granted, your knowledge isn't so high, because you question how evil can exist in the world if God made it. For one, you ask a question that has been answered a million times. Your potential for finding the answer is easily there. You've been blessed with answers and knowledge. Now, to whom much is given, much is required.
Regarding evil's existence further: God doesn't associate with the wicked. No one who is supposedly righteous supposedly does. Imagine a Senator or some other Congressman giving earmarks to a Neo-Nazi group, or one running for President who sits in a church where the preacher spouts blatantly stupid, racist, wicked things. It tarnishes the name. Likewise, God's hand of blessing doesn't stretch to the wicked. (Although, humans are conceived of love: God probably did it for the sake of Adam.)