I agree that there should be だ before と言われています. This is an example of だ抜き, and generally it should be avoided in formal texts like this. But this happens often today, and I won't call this a big mistake. Many people won't even notice this.
Because speaking casually very often means discarding the question mark か as well, making the casual version of そうなんですか？ -> そうなんだ？
It's just not そうなんだか, but "だか" that you wouldn't hear in any sentence, because you would simply stop at だ。
Broadly, で is just the conjunctive form of だ・です, as in "[statement 1] is, and [statement 2]". The ある after that, if used to end the sentence, is just the copular ある: "is, am, are, will be" etc. This kind of usage is rather stuffy and formal, and archaic.
In most cases in modern Japanese, you'll see である not at the end of a sentence, but ...
The grammar follows your second pattern. The structure 〜でも translates to "even__" (source: Makino & Tsutsui, Dictionary of Basic Japanese Grammar, page 111), or more idiomatically in this particular case, "__ at all."
何___ない translates literally to "no what" (nothing). Just as we say "nowhere" to mean "no ...
Also most adjectives that end with い end in ん
Everything else (non い) なんです
It seems there are exceptions like 得意(とくい) but that is still
なん so it takes some getting used to