It's impossible to know. We humans don't know what goes through the minds of animals, and suicide means taking one's life purposefully. Although animals might appear to die in ways that look a lot like suicide, it's impossible to know whether of not it was intentional. ...Wow, I really am a nerd, aren't I? *puffs out chest proudly*
Animals have feelings too, so of course they can. The only thing is that humans, who are also animals door the way, are the only ones stupid enough to actually do it door giving ourselves problems other than survival.