Learn English – Was Already vs Already Was

Prescriptive English grammar, as I was taught it in 1962, requires the use of the past perfect tense following a verb in the past tense. Therefore, by this prescriptive formula, only "I didn't know it had started already!" is acceptable. However, grammar changes based on usage. Descriptive grammar, the rules that govern spoken informal English, seems to be moving away from the use of the past perfect tense, at least in the US. Word Processor applications underline "had had" in red, in the expression,"He had had enough." So, my answer to your question is, it doesn't matter which expression you use, unless your audience objects. My own preference is to place the word "already" after the auxiliary verb "had", which sounds more euphonious: "I didn't know it had already started!"

The correct form would be

John was troubled by something but I didn't know what it was.

English usually forms sentences with a subject-verb-object structure, as in your first clause:

John (subject) was troubled (verb) by something (object)

The second clause is a little more complex:

I (subject) didn't know (verb) what it (object) was.

"what it was" here is an adjunct clause with "what" as a subordinate conjunction, which modifies the matrix clause "I didn't know".

Note that if you were to turn this into a question, you would use subject-auxiliary inversion:

What was it?

(Disclaimer: there are a number of grammatical topics covered here and it's almost certain that I've made a mistake somewhere along the line, so please feel free to edit the answer or comment pointing out anything I haven't explained properly).