Sorry, I don't have any pictures at the moment. My bike is currently disassembled. In your original post, you said you wanted to position your front brake hose and rear derailleur cable on your right shifter. Your last picture shows your front brake on the left shifter. Looks fine through the handlebars and stem. Your front brake line and front derailleur cable shouldn't have to cross each other at all though.
Could you explain what you mean by saying automatically turns in one direction?