In the sense of "has internal workings that are not directly observable [at least in practice]", yes, emotions are a black box (or may be usefully treated as one, at least). But you can learn to predict the behavior of a black box, given particular inputs, even without understanding of its internals.

I don't perceive much difference between the dysfunctional feelings produced by mental illnesses and the feelings produced by everyday experiences, except that one is unpleasant and interferes with function to an unusual degree. But if a loved one of yours died tomorrow, those feelings would be unpleasant and interfere with function, too - it's only the normality of that unpleasantness and interference that separates the feelings of normal grief from those of depression.

When you say "feelings that happen for no good reason" in reference specifically to mental-illness-related feelings, I think you're sort of missing the point - no feeling happens for "a good reason" except perhaps in some broader evolutionary sense. Feeling and reason are wholly separate and incommensurable categories. If you say "I'm sad because my friend died", you are making a category error: you are sad, period, end of sentence. That is why, among other things, you become less sad as time passes after your friend dies - regulatory processes in your emotions are returning you to an emotional set-point, even though none of the "reasons" to be sad have changed (your friend is still dead, you still miss them, you still have things you can't do with them, etc).

It's not that being sad after your friend dies isn't a predictable emotional response, it's that the apparent logic and the response are separate, in the same way that the movement of a hurricane is predictable but carries no logic or intent. A hurricane doesn't weaken or strengthen, turn or move straight, because it's logical to - it just does so according to the particular dynamics that drive it. And while those dynamics may be analyzed by reason, they are not, themselves, driven by it, nor do they carry it. And so it is with emotions: any logic they carry is in our external understanding of the patterns of the black box, not something contained within it, and the fact that a black box may or may not happen to behave similarly to other peoples' black boxes is incidental.

I'm not arguing that you shouldn't or can't try to understand emotions from the rational side of yourself. I'm arguing that reasoned understanding of emotions is always "from the outside", while experience of emotions is "from the inside", and that the two are fundamentally different things. And I mean this more as a practical claim for living as a being with qualia than as any sort of philosophical claim - it's a way to understand and approach your emotions, not some claim about the Universe.