Do you think precise translation need a special mood?

Translation relies basically on how much you are focused on the document that you are working at. So concentration is the key for a good quality work and there are different methods that people use to enhance the concentration level. Personally, I listen to music while translation. It helps me to focus and not to be distracted by the outer environment.

I don't so! You just need to double check your draft. But maybe for interpreting and other vocal translations.