It can be. Some words can be seen both hyphenated and non-hyphenated.
yes
The hyphenated version "non-driven" is correct.
No it shouldn't be.
is nonpublic one word
Soy milk is an example of non-dairy milk.
dairy is renewable
It should be hyphenated: non-weight bearing.
Silly but true, it´s ´non-dairy products´.
The prefix "non" should be hyphenated when it precedes a proper noun or when it helps clarify the meaning of the word it modifies. For example, "non-English" is hyphenated to specify that it refers to something not related to the English language. In contrast, "nonprofit" is typically written as one word without a hyphen. Always consider clarity and readability when deciding whether to hyphenate.
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.