On the first screen of each skills page, when you've chosen a skill but before you actually start doing the individual lessons on it.
Only visible on the website (and if you have a large enough screen).
Not included in the mobile apps, nor (apparently) when the website is viewed on a smartphone browser with a screen that's "too small" -- one reason why I consider the apps to be unsuitable for learning a language on Duolingo as all the lesson notes and grammar explanations are hidden from you, though they may be useful for practising a lesson you have learned through the website.
That would have to be "ένα επίθετο". If you are referring to the hint "an adjective" that might be used in a sentence where the English required an article. Not all hints are viable for each exercise as in a dictionary you might find a variety of definitions for a word but not all will be correct for what you want to express.
With the Duo hints it's safest to choose the first word. That's usually the one needed for the sentence it's under.