Ran-
Regarding your questions, it never occured to me that the right hillock could be totally manmade. Certainly the dirt from the excavated bunkers could have been pushed around a bit, but that area around the 4th tee is about as close as you get to the visible existing dunes adjacaent to the course, so it seems plausible that it was there originally. Except for the 13th complex, of course.
Behind the 15th directly are bunkers, the 2nd green, and then the wall. The buckthorn is on the other side of the wall, so I don't know if that is the club's property. HCEG owns most of the land between the course and the Firth, though. Also, the non-native, invasive buckthorn does shield the course from residential views in Gullane. You can occasionally hear people singing or talking on the phone in their gardens coming up the 2nd fairway. The picture I posted clearly does not give you the best view, which is better from the left tee or the high sand hill in between the left and right tee locations.
So whether the view would be improved or not with the removal of the buckthorn is quite the conundrum--trees and a bit of water view or a lot of water and a bit of housing.
There has been talk around Gullane about removing as much buckthorn as possible from the various golf courses becuase of its negative impact on the bird life in the area, with one scenario including the reintroduction of a certain highland sheep variety to keep the overgrowth away after it has been cleared! Unlikely, but fun to imagine Gullane Hill with grazing once again.
As for the 15th green, it is likely the most interesting on the course in my estimation as well, along with the 2nd, 5th, 8th, and 11th. I do have more pictures as well, and I will try and post some as (if?) they become topically relevant.
Interestingly, the 2nd and 15th greens are right next to each other, as are the 5th and 11th greens. I suppose it logically follows that these areas had nice subtle contours when the holes were conceived.