Does the free will exist? No present research provides any evidence for or against. The idea that the free will does not exist is based on a lack of understanding how complex dynamical systems like the brain work.
Is a thought simply the sum total of the activity of all the neurons in the brain? No, just as a message is not simply the placement of a sequence of letters which follow the rules of grammar. How do those letters stand in relation to that message? How does the activity of neurons stand in relation to a thought? Was Descartes right, or are we our brain?
What causes your depression: serotonin or what you experience? The answer: the question is invalid! Both play a role, and are interconnected. You cannot say that one of these is the cause.