2. Before going to bed, I always brush my teeth. (Your sentence is simply not natural. There is no point in correcting it when no native speaker would say it.) We go to church, to school, to bed (and a few others) when the emphasis is on the activity - to worship, to learn, to sleep. If you say "to the church" you mean you are travelling to the buildling, but not for worship. If you say "to the school" it means to the building, but not to attend classes. If you say "to the bed" you are going to that piece of furniture, but not for the purpose of sleeping.
3. The doctor. It's a common noun, so it requires an article. Dr. Jones is a proper noun, so you don't have an article.