Why does the translation of triste underneath the word in Duolingo then say depressed and disreputable if they are not valid translations?
You might as well get used to it - the hints they give are frequently very misleading and should not be relied on. Some of these suggestions are very, VERY specific and not useful in any ordinary context.
I once saw "bed" as a suggested translation for the word "siège", which generally means "seat". I did some research and discovered it is used to refer to the "bed" of crushed rock and stuff that a railroad sits on, or the foundation that asphalt is spread on to make a road - in short, a "road bed". It never means the thing you sleep on.
So - a word to the wise. The hints are somewhat useful when you look at a word and it looks familiar but you can't quite recall what it means. For any other purpose, you're much better off using a good dictionary.
No, "triste" is invariable (it works for feminine and masculine nouns alike).