There are situations where it would be hard to discern if non-human animals were comitting suicide or dying of natural causes. For example, refusal to eat could be suicidal or just that they feel too sick to eat. Whales that beach themselves and are then dragged back into water sometimes re-beach themselves, and nobody knows why. It could be a screwed up processing of direction, or they could be attempting suicide. The suicide aspect has been speculated upon, but we have no way to know. And there are those darned squirrels playing chicken in the roadways. You ask a tough question.
The mirror question is probably easier to answer. But, even then, it's hard to know if the animals recognize themselves or think it's another of their species they are seeing (if you put a mirror up by a betta's fishbowl, you'll see it try to attack the reflection...the top of a dresser with a mirror is not a good home for a betta's bowl! Anyway, it's an example of the fish thinking the reflection is another fish, not recognizing it as itself. I'm not sure if even human babies realize their reflection is themself until they learn this from a parent...my friend's 14 mo old has recently learned to give kisses to other people and we watched in amusement as she tried to kiss the little girl she saw reflected in the surface of a glass table...she clearly didn't recognize the reflection as herself).