Can Sasuke's Amaterasu go through windows? I am not sure on whether you need to just see the object you want to cast it on, or if there must be a physically clear path to it.

Can the Amaterasu go through windows?
Yes, Amaterasu can pass through clear glass.

To quote the wiki


  Amaterasu produces black flames at the focal point of the user's vision.
  - chapter 390 page 3


The focal point of a users vision is located at the back of the on the retina as seen on the image below.

This means that whatever is being 'seen' by a user at that time, will be cast ablaze. Comparable to how you can either focus on something beyond a window, or if the window is dirty, the window it self.