Animals' Perception of Death & Pain
Most animals don't understand death; they don't know it's the end of life. Their understanding of their own death, when they have to face it, is shaped by how they understand others' death. When it happens to another animal, they become confused, not knowing whether it's asleep, apathetic, meek, submissive, playful, or just ignoring them. They stay close for a while, sad for the lack of response, hoping it might change. Gradually, as it gets smelly, they avoid the smell, or try to clean the area, hide/bury the body, then move away. They occasionally return to the site of their dead, until they forget them.
However, intelligent animals with a more powerful memory can suffer more, mostly because of their recollection of their dead and their recurring images. Still they don't know what happened, where they went, or if they will ever come back.
Intelligent animals are not so different from unintelligent or uneducated humans who "wouldn't" understand death. Most superstitious humans refuse to accept death, even those who are intelligent.
However, when an animal's death is not caused by a natural cause like aging or a fatal disease, but rather by an accident or predator attack (e.g. a mother chimp watching her child being eaten by a lion), it's different. They see a loved one vanishing slowly, giving them a vague idea of what death is like, but such memory is not shared, explained, or investigated, as humans can do thanks to their advanced language, social straucture, and scientific data they have. .
Animals don't understand "dying" either; they only think it's a form of extreme pain they must avoid. When it happens, they don't understand that they fight the battle of their life, as some documentaries dramatically show. Even when they die naturally, of aging or diseases, they feel themselves getting weaker and slower, but they can't see their approaching end.
Saying that "animals don't know they exist" is not without a reason. Animals don't know they exist now, because they don't know they won't exist later and they hadn't existed before. However, this doesn't deprive animals of feelings. Animals are not lifeless robots, just following their genetic "programming," because they can still feel their existence. They have senses enabling them to feel life powerfully, although they don't have a willpower like us, that derives from reason (mindful existence). They don't stop, think and decide; they just follow instinct. When people are under drug influence or just going by instinct, they don't know they exist either: they are not so different from animals then.
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Animals' emotions are more simple than ours, even though they share most of our physical and social pleasures and sufferings. Their feelings are simple because their brains are. We know that memories, satisfaction, expectation, attitude, etc. are all ingredients of happiness that depend on a person's brain and its content. Animals' brains are not developed enough to store and process many data, outside from the hear and now. They don't conceive feelings the way we do, after perceiving them through senses.
As for animals at the bottom of evolution hierarchy, such primitive life forms can't feel pain or pleasure because they have no developed nervous systems allowing neurotransmitters between the brain and the rest of the body. Only starting from the more evolved insects, they begin to experience such feelings.
All living beings have rights as long as they can "enjoy" such rights. We know that many animals are capable of pain and pleasure, some are not (e.g. bacteria), and some we are not yet sure about (e.g. many worms and insects). When an animal's neural anatomy and nervous response are unknown yet, it is safer to treat it humanely, as capable of pain and pleasure, until proven otherwise by science.