Since God knows all the harm that wicked people and demons cause, why does he permit them to exist at all, or at least knowing the evil they would do, not destroy them before or at least after they do it?

While a brief column such as this cannot possibly plumb the depths of the questions you raise, a few observations should be made. 
 
First, it does not pertain to God to annihilate any rational creature he has made. Thus, angels and men have an immortality that pertains to their souls; and for humans, one day, to our bodies as well. Having given the gift of life, God never withdraws his gift. While it is true that demons, and the human souls in hell have definitively rejected his love, God does not thereby cancel the love he has extended to them. He continues to sustain the life even of his enemies, though they choose to live apart from him and what he values. 
 
Secondly, your question tends to put God within serial time, where time passes incrementally from future to present to past. And, thus, the question occurs to us, "Why would God at some time in the past, knowing what a person would do in the future, bring them into existence today?” But God does not live in or relate to time in this manner. For God, past, present and future are all equally present. And thus, while God's inner life is mysterious, it is clear to us that God does not deliberate in the manner we do. Time does not unfold for God like it does for us. So, to some degree, even the way we phrase our questions is invalid. God does not ponder “A”, look forward to “B”, and then do “C”. 
 
But let us for a moment assume God did act temporally in this way, and that at some point in the past, God, knowing that a person would do horrible things in the future, considers their existence today. Let us say, that seeing the bad things they would do, he simply vetoes their existence. 
 
But what does this do then to human freedom? In effect, it cancels it. Why? Because if in knowing that a person will choose badly, God preemptively vetoes their existence, then the whole process of choosing God and his kingdom values is “front‐loaded” and none of us who do exist are really free. Freedom would only be theoretical since no existing person actually can or ever did say “no.” If we are not free to say no, we are not really free to say yes to God and love Him. 
 
Many more things related to the questions you raise could be said. But for now, let it be enough for us to say that the answers are caught up in the mysteries of God's love, time, and human freedom.