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It can be. Some words can be seen both hyphenated and non-hyphenated.
yes
The hyphenated version "non-driven" is correct.
No it doesn't need to be hyphenated.
No it doesn't need to be hyphenated.
No it shouldn't be.
is nonpublic one word
It should be hyphenated: non-weight bearing.
The noun phrase 'four week vacation' does not need to be hyphenated.
yes for clarification
The hyphenated non-school would be correct, but would be an unusual usage.
Yes. "Non" is not a word in its own right, and only exists as a hyphenated element.