"I would like to take a break."
Because "take a break" is a phrase and if you look up the definition of each word "break" is the only one that would help at all, but even that has a long list of meanings - if Duo listed them all you'd have: 打破, 断, 决裂, 切断, 拆散, 决口... The "hints" can be helpful for somethings but for phases like this they're not really going to help.
Would 我想休息, dropping the 一下 from the answer, have the same meaning as the English phrase?
I think "to rest" only implies inactivity/ relaxing for an indeterminate period of time (you might resume the activity after or you might do something else) while "take a break" implies a short period of rest and then the activity resumes. And I think that also describes the difference between "休息" and "休息一下".
I ran 休息一下 through a translator the results were 'take a break'. I ran 'I want to rest a little' through the translator the results were '我想休息一下‘. Looks like the same characters may be translated two ways.
As a native english speaker 'taking a break' and 'resting a little', have different meanings. When I take a 'break', I stop the current activity and do something else: stop studying, then go eat a sandwich. When I 'rest' a little, I stop the activity and do no activities: stop studying, then go take a nap.
There must be some way to indicate these differences in Chinese. Can any native Chinese speakers clarify?
Not a native speaker, but I'm pretty the way it works is 一下 "a little" is needed to make 休息 "rest" more finite: "I want to rest" vs "I want to rest for a bit (and then get back to work)". You can think of 休息 here as "rest (from the task at hand)/ stop doing work" rather than, say, sleeping.
I really dont see a difference between " taking a break" and "taking a short rest". Same with Chinese, its all context.
I studied in China and all my chinese teachers would only speak "我想休息" without the "一下儿"
Yes the hints will often not be applicable to this exercise, as I think they are usually just dictionary-based. This applies to all the Duo courses, although in some courses the first hint is often useful as if someone has tailored the first hint to actually be helpful (I don't know if that is actually possible though).