They do, they just don't have eyelids. And it seems they can also have some simple fun.
But understanding the concept of own death requires some ability to imagine future, and that's what even many people have problem with.
Sure but we can treat most illnesses that's why our life expectancy is late 70s.
Have you ever seen a deer doing chemotherapy? No, they just wander off into the woods and die.
It has to do with food being damaging to teeth (starch and sugars instead of protein)
Deer just die when their teeth wear out and they can't digest food anymore