The Natural History of Selborne was written in 1789, so one must be aware that the English language used in this book is over 224 years old. The older meaning of words, and/or their meaning specific to southern England, must be taken into consideration.
(1) "Down," (usually, downs) especially in southern England, refers to an open, rolling, upland country with fairly smooth slopes usually covered with grass. "Sheep down," would therefore likely mean an open grassy area with rolling slopes where sheep graze.
(2) "Hanging Wood" is probably an area on a cliff covered by a growth of trees. To the observer, the trees growing off the side of a cliff would look like "hanging" trees, hence the name "Hanger."
(3) "High Wood" is probably an area that is covered with tall trees. "Wood" is an area of land, smaller than a forest, that is covered with growing trees.