Yes, it's a proverb. Basically, it means that you have to make do with what you have. It's commonly attributed to Cajsa Warg, who wrote a very widespread cookbook in the 18th century, but she never actually used the phrase. Both occurrences of man refer to the same person.
I mean that the parenthesis and additional word (to offer), not in the actual translation be included...perhaps below the actual translation. Idioms in the duolingo spanish class are difficult because they only have an american translation and not a direct one. In spanish, one often misses the beauty of the idiom as it is stated in its original language. It seems like this is the opposite. Sometimes it is good to see both together. It helps to understand word order and translation between cultures.
I agree. "One takes what one has" is not idiomatic for me, either. (Maybe it is the way to say it in other English-speaking places. I don't know.) Where I live, we use a couple of set phrases, just slightly different from what you suggested:
You take what you can get.
You make do with what you have.