My DS6 went through the same thing and still asks about death and the eventual end of our planet and galaxy. He too started out the school year telling people at school he hated himself and he was stupid. It seems young to have these feelings, but these kids are special in that they can think deeply and question things on an unusual level. You definitely aren't alone!
He has a lot of anxiety, especially around bedtime when he has to be quiet with his racing mind. Many of the things she worries about translates to anxiety which is super common in gifted kids. We've found that listening to a bedtime meditation helps focus those thoughts on something so he can more easily go to sleep. It has made an incredible difference even in his awake time. It took a few weeks for it to really show a difference, but now he doesn't like to go to sleep without it. His favorite is '"Bedtime Relaxation for Kids" by Christianne Kerr (sp?)
We've also met with Dr. Dan Peters when we were going for testing. He recently released a wonderful book called "The Worry Monster". I highly recommend taking a look at that book as well.
