Believe it or not, but this is actually a controversial area in the animale behaviorism field. When I got my training as a cat behaviorist, the warning to not 'anthropomorphize' was dropped like every 5 minutes. Though there are more scientists in the field that are agreeing that animals do have feelings, and probably a lot more deeply than was previously assumed, 20 years ago, those same scientists were ridiculed for being softies and unscientific as you cannot prove that animals have emotions since you cannot ask them and you are reduced to deducing their actions.
However, more and more scientists are actually making documentaries of the remarkable behavior as listed above. There is amongst others a documentary somewhere of how family oriented elephants are, how they stay with an injured or handicapped herd member, despite the fact that it slows them down and causes problems with finding food and water, how they visit their dead, and...well, how they appear to be able to be traumatized by what happens to them when their moms are slaughtered in front of their eyes.
I remember a particular documentary where a group of baby elephants that had likely been traumatized that way became what is known as 'manhunters'. They sought out humans to kill..in what seemed to be a murderous rage.
In another documentary, they had not killed the mothers, but because they at that point in time lacked the technology to transport adult elephants, they separated the young elephants from the adults in the herds to reintroduce the herd in a place where elephants had all but disappeared. A noble return to the wild action. Unfortunately, about a decade later, that same group of elephants became a real problem...as they started killing rhinos for the heck of it. The people who had done the re-introduction had not accounted for the fact that elephants are family oriented groups, meaning that the elderly are respected and in charge of a herd normally. By releasing only babies, they had basically let loose a bunch of rowdy teenagers and it was the teenage bulls who were killing the rhinos...out of competition? Boredom? For fun? To strut their stuff? Nobody knows. The thing is that they finally had the tech to transport a full grown elephant..so they introduced a couple of adults, amongst which a bull in 'mussh'. The second they got wind of him, they piped down immediately and the peace returned in the reserve.
It is still not clear how deep and which emotions animals experience though. If you take a cat, for instance, they are missing the frontal lobe development that humans have. This could indicate that they are incapable of complex emotions such as self-pity. It also seems that their pain indicators are straightly linked to the brain, causing them to apparently just experience the pain, act on it 'rationally' aka the survival instinct kicks (do not show weakness and hide to heal), whereas humans are a lot more likely to complain and whine about it (due to the herd mechanism we have), and experience a multitude of emotional turmoil.
Unfortunately, all of the above is *still* just a hypothesis..we just don't know.
Its funny that scientists in the past were unable to admit the 'we just don't know' and go the ' if we cant prove it it cannot be there' route