re: elephants in post above- Hence the book "When Elephants Cry". The author's name I do not have in front of me but it came out about 8 years ago. Subject is on animals and emotions (obviously!!).
About the ape family in particular, you should go to koko.org and ask Penny. She has been with gorillas for 30+ years now. I remember in one of the koko documentaries seeing her wail and wail over losing her 1st male companion, Michael, who she refused to mate with but they had a relationship that was important enough to her that it hurt her deeply. She dragged his blankets into her bed and lay with them for I don't know how long.
Same when her kitten died (cat by then i think), she wailed this horribly heartbreaking wail all night long.....it's clear that they feel emotional pain as we do. But, oddly enough, I've never seen or heard a discussion about actual tears! I encourage you to ask Penny about gorillas! Very Good Question!