While it is true that God is love (1 John 4:16), it is also true that He is just in all of His ways (Deuteronomy 32:4). Therefore, it is necessary to examine these verses in light of what we know of the LORD’s character. Proverbs 6:16-17 taken woodenly could be construed to say that God hates sinners, but that is not the case. The writer is using different parts of the body to personify the evil things and behaviors that God detests. Psalm 5:4 is quite simply a statement of truth: God cannot dwell with the wicked because He is Holy in all of His ways. Just as He had to hide Moses from His glory (Exodus 33:18-23), God’s Holiness and purity are so great that no man can stand before Him and live. Therefore, it would be impossible for the wicked to live near God’s presence. Now of course, it goes without saying that this verse is also pointing to the very real fact that we cannot go before the presence of God and continue in our wicked ways. Again, in Psalm 11:5 we should examine it from the standpoint of “Why does God hate the wicked?” The simple answer is because they are violent and wicked! Were they not, He would not hate them.
The Bible is replete with instances where God has been merciful to those who have been sinful and wicked. Consider the beauty of the book of Hosea, where Gomer’s children are given names that signify that they are not accepted by God, only to be given acceptance and love by the Almighty (Hosea 1 and 2). Consider as well the example of the Assyrians who were spared by the LORD from His anger by their repentance. God does, indeed, love the sinner, though He hates the sin. The problem is that often times the sinner is all too willing to continue in their behavior. It is this continued desire for wickedness that God abhors. Perhaps it would be best to consider what 1 Corinthians 13 says about love. Paul describes love as being patient, kind, not boastful, not proud, not easily angered, not delighting in evil, but rejoicing in truth. When we consider these descriptions of love, then think about the fact that God IS love, then we get a clearer picture of who God is. He does not delight in wrongdoing, and in His perfection and holiness, He alone is right and just in carrying out judgment on those who are evil. To fully answer your first question, God does in fact love the sinner despite hating the sin and is fully just in His way of dealing with sin (and, by extension, sinners who decide in their hearts not to repent of the sins that God abhors).
While I can’t claim to know the answer to the question of whether or not people are created for destruction (Answering that question would solve 400 years of arguments between Calvinists and Arminians), I do tend to favor the idea that God does not create people simply to hate them. For the limits of time and space, this is not an easy issue, and as I have said, many people have tried to answer this question. Some great resources available to work through these issues are (for the Pro-Arminian lean) Why I Am not a Calvinist by Jerry Walls and Joseph Dongell, The Quest for Truth by F. Leroy Forlines (Great because it also addresses modern and postmodern philosophy), and (for the Pro-Calvinist lean) Why I Am not an Arminian by Robert Peterson and Michael Williams. Out of the three, I found the book by Forlines to be the most well-thought out, researched, and painstakingly laid out in such a way as to present an educated assessment of the two sides. In the end though, this is the type of issue that should not divide Christians. We can debate vigorously, but must never divide over issues that do not compromise the core of the Gospel.