Some of the trees are hotwired and other areas are sporadically "wired off" to allow for regeneration. That said, there is always large areas of vegetation that are not protected and the gorillas have plenty of access to the vegetation. I have never seen any of the adult gorillas climb the trees, although when the troope has infants they regularly do (and have been allowed to destroy a few mature trees in the past as well!).
whilst the exhibit does have its spots where the animals can get away from the direct glare of the public or at least keep a large distance from them, they are most often found directly in front of the public at the first two viewing areas, one of which is large glass viewing windows. There are five vantage points at which to look into the gorilla exhibit. however, a tip - the second glass window area, after the treetop monkeys and apes virtually never has anyone there as its a detour off the main path and most people already had a look at the gorillas on the other side of the exhibit. Its a great spot for some quiet personal viewing. and features parts of the exhibit rarely seen by most such as the pool and waterfall.