「どうやらここで間違いなかったようですねえ。」。
For どうやら, my dictionary says to see 何とか and it means "something" or "barely", "hardly". Someone says it means "apparently", "somehow", like なんとなく, I think. Maybe it's mistyped and I should see なんとなく. I don't know.
In modern Japanese, どうやら means "apparently", "seemingly", "it looks like ～" in nearly all cases. It's typically used with ～ようだ, ～みたいだ or ～らしい. If you are new to this word, you have to master this meaning first. どうやら in your example is used in this sense, too. Of course なんとか does not have this meaning, so どうやら and なんとか are almost never interchangeable.
However, どうやら occasionally means "after a long time, although still not perfectly", "to barely manage to ～" or "to somehow manage to ～", as in the following examples:
- どうやら完成までこぎつけた (from デジタル大辞泉)
- どうやらこれで水漏れが止まりそうだ (from 明鏡国語辞典)
- どうやら日本の生活になれてきた (from JLPT先生)
In this case, the meaning of どうやら does overlap that of どうにか and なんとか. But most people use どうにか/なんとか today for this meaning, so maybe you can choose to learn this meaning of どうやら later. FWIW, I personally never use どうやら in this sense.
なんとなく means "somehow", "kinda" as in "I somehow feel". It's a much weaker expression than どうやら.
- なんとなく彼が勝ちそうです。
(I don't know why but) I somehow feel he will win. - どうやら彼が勝ちそうです。
Apparently, he will win. - どうやら彼は勝った。
Apparently, he won.
(Rarely: He somehow managed to win.) - なんとか彼は勝った。
どうにか彼は勝った。
He somehow managed to win.
