Yes it should be hyphenated.
Yes it should be hyphenated: well-liked.
It should be hyphenated when it's an adjective.
It should be hyphenated when it is being used as an adjective.
Yes, well-being is a hyphenated word.
No, "a well know" is not a correct phrase. It should be "a well-known" with a hyphen to make it an adjective.
No.
Yes!
Here is an example of using a hyphen correctly: Justin was purpose-driven by his motivation to finish well.
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You should hyphenate well nourished and well developed IF followed by a noun - i.e., "well-nourished and well-developed man" or "well-nourished and well-developed patient". If the noun is before these, then you would not hyphenate - i.e., "The patient is well nourished and well developed". This would also be true for the following: "well-healed scar" or "the scar is well healed". Answer provided by a medical transcriptionist with 18 years experience.
Not usually. Many compound words do begin with hyphenation, and co-operate is an example. Without the hyphen, it might be pronounced "cooper eight". Once the word is sufficiently well recognised, the hyphen is used less and less, so that many people nowadays write "cooperate".