No, it's not necessarily wrong to question God -- not if we're sincerely seeking answers. (Unfortunately, some people aren't really interested in getting answers to their questions about God; their "questions" are merely an excuse to keep Him at a distance.)
Evil is real; it isn't just an illusion or something we do out of ignorance. But evil doesn't come from God, and we shouldn't blame Him when people do evil. Evil comes ultimately from Satan, whose goal is to oppose God in every way he can. Satan isn't a harmless cartoon character running around with a pitchfork and red suit. He is an evil, powerful spiritual being who does everything he can to deceive and destroy us. Jesus called him "a murderer from the beginning ... and the father of lies" (John 8:44).
But evil also comes from within us -- from our own hearts and minds.
When we do something evil (such as abuse a child), God isn't to blame for it; we are. The Bible says, "When tempted (to do evil), no one should say, 'God is tempting me.' ... Each one is tempted when, by his own evil desire, he is dragged away and enticed" (James 1:13-14).
Does this mean we can never break free of evil? No, not at all -- and the reason is because Jesus Christ came to free us from sin's power over us. Commit your life to Him and ask Him to forgive and change you -- beginning today.