Say if one wanted to allow their fan base to comment on album pictures only and not profile pictures, would this be possible? I know that in the personal profile, privacy options are available. Is there anything similar for fan pages?
No, it is not possible to set privacy options for the Page's Profile Pictures at all as they are "Public" by default. Facebook does not allows any such change. This kind of privacy would un-root the very essence of a Page. This of the picture to be required to be public in the same way as the Page's name, the page's visibility to others, your Name on your Facebook profile/timeline being visible to everyone.
Similarly, there are no privacy options available for the Cover Photos in the new Facebook Timeline.