1) Yes, it's fine. Semicolons are OK wherever there is a full stop intonation; they indicate that "there is still some question about the preceding full sentence; something needs to be added", as Lewis Thomas puts it.
2) "No;" is called an Utterance. As you point out, it's not a clause -- no subject, no verb, etc. -- much less a sentence. But it does get full-stop intonation, and it's exactly the sort of definitive but uninformational utterance that invite a semicolon to mark the explanation or other expansion of the utterance. But only in writing -- in speech we can't tell semicolons from periods anyway.
3) The usage of semicolons is described by saying it requires a full-stop intonation. That's not exactly grammatical, but it does have the benefit of being true. If you pronounce n utterance that's correctly punctuated with a semicolon, it will be indistinguishable audibly from a period, or full stop.
That's all because semicolons are technological, not grammatical. Grammar is about real, i.e, spoken language, not written language; written language represents spoken language, not the other way around.
Pronunciation often shapes, and masks, the punctuation, spelling, and formal usages of an orthography; a good example is the similarities and differences between definitive and indefinite articles in English.
Everybody knows that there are two versions of the indefinite article: a and an.
Fewer people know the actual rule for their use, though native speakers can be said to "know" it in some way, because they use it correctly. It's simple, but requires one to consider pronunciation:
a /ə/ occurs before phonetic consonants, and an /ən/ before phonetic vowels.
Spelling is irrelevant; an hour but a utility.
Fewer people still, however -- most of them non-native speakers -- know that there is a completely parallel rule for definite article: the and the
the is pronounced /ðə/ before phonetic consonants and /ði/ before phonetic vowels.
Spelling is equally irrelevant: it's /ði'awr/ but /ðəyu'tɪləti/. However, native speakers rarely notice this difference in pronunciation, thinking of both the's as "the same word" because they're spelled the same. If they are both "the same word", then so are a and an.