The Fall/sin, free will, Satan/demons, etc. are part of the explanation for some of these things. It is a wrong assumption that homosexuality, mental illness, etc. is innate, genetic. I know Down's syndrome kids with limited mental capacity who know and love Jesus. Those who lack mental/moral capacity can still go to heaven based on non-rejection of Christ. Gen. 18:25 The judge of all the earth will do the right thing and judge according to capacity and light (some have great light and reject it, while others have little light, respond to it, get more light). The Bible is clear about people like you and I who have opportunity to hear the gospel, but reject it. Even those who have not heard the name of Jesus (the only way to eternal life) are condemned and without excuse (Rom. 1-5).
There are many resources on the problem of evil with good biblical, philosophical answers. This is not the issue to be hung up on. THe issue is whether we receive or reject Christ, a yes/no answer based on faith/knowledge, not theological perfection. God will triumph over evil in the end, but there are reasons He does not always judge it temporally, immediately (we would all be instantly dead in light of His holiness). Free will is finite, but irrevocable if it is to be genuine. Love is not possible without free will. Having great capacity for love and good implies great capacity for evil, selfishness, hatred, etc. We will all give an account, so justice delayed is not justice denied.
The WT is not theologically sophisticated and relies on 'Christendom's' publications (which they distort anyway). I would be interested in their concept of original sin (if any), evil, etc. Usually, they have simplistic answers that appeal to simple people, but lack depth of critical thinking, etc.