I am confused about when you do and do not need to use line 10. Would you use line 10 if you are claiming eligibility for treaty benefits based on the fact that you do not have a PE in the U.S. under the relevant treaty; or are the general reps of line 9 and the certification at the end enough?

Yes, you would use line 10 to claim that you do not have a PE in the U.S. You need to get an EIN to claim treaty benefits.