As someone replied before me, "Non si sa mai" is a common idiomatic expression which is the equivalent of the English "You never know". Mainly used in colloquial language.
Notice that this sort of idiomatic expressions, of which there are a number in Italian language, usually don't follow a specific grammatical pattern, so they can be somehow an "exception" to the rules.
I suggest you to learn them by heart, and focus instead on their usage in context rather than on the grammar.
In these specific expressions the si particle is not used as a reflexive pronoun, but as a non-personal pronoun ("pronome impersonale"), exactly as mann in German or on in French.
Said this, I'm going now to comment your questions:
[...] shouldn't it be: "Si non ne parla"?
No. Let's analyze the phrase logically, and let's suppose by absurd that:
- The subject would be "he/she" (it's implied, since "parla" is a III sing. person verb). (Hypothesys).
There would be a discrepance between the subject, the ne particle and the impersonal pronoun si, because if the subject is "he/she" it is then uncorrect to use a non-personal pronoun; this causes the phrase to sound weird, and to be semantically incorrect.
In other words, your mistake (which is perfectly understandable, as I said at the beginning) is simply logic: you did not negate the proposition properly.
Se ne parla --> Non se ne parla
Where se is exactly the same of si impersonal.
I know that (or at least I was told; correct me if I am wrong) in
Italian, you say: Si non lo sa mai
It's again a matter of logical analysys of the phrase, as described in question No. 1;
Lo si sa (sempre) ---> Non lo si sa (mai)
Please note that words order in Italian is, sometimes, particulary relevant, especially if you want to sound "natural".
I was told that you would not say: Non se lo sa mai, So why can't the same be said for Non se ne parla.
- Non (negative p.) se (subject, impersonal p.) ne ("of it") parla (predicate, III sing).
- Non (negation) lo (object) si (subject, impersonal) sa (predicate) mai (adverb).
Note that the pattern Subject --> Predicate --> ... --> Adverb(s) is the standard sentences pattern in Italian.
I hope to have been helpful - and exaustive.
Sorry for my English, though!