"Does sin block my prayers?"

Thank you for what you taught me about relationships. My husband passed away recently, and I'm so grateful to know the truth. Can God still hear our prayers if there is sin in our lives? Does God ever hear the prayers of an unbeliever? Am I forgiven of a sin even if I do it again? Was my repentance not legitimate? One of our church leaders has a drug addiction. I'm wondering if he should still be teaching others?