In what contexts can this be used? Can it be used with food, time, difficulty?
All of it. Usually, it is accompanied with "thôi": "chỉ một chút thôi!" and you can use it with emotions, time, amount of food/drink, difficulty, pretty much everything (can't think of an exception now).
You can also use một lát for a little bit of time or một tí.
just a note: Perfectly fine translation, but we USUALLY add "bit" at the end. "Just a little bit." In all different contexts, it's just a figure of speech.
I said only "a lttle" without the "just" and was marked wrong with the remark that the article "a" is needed here?!?!?!?!