Eden,
You are absolutely correct. You will find discussions on whether the inserted "is" is valid and whether the rendering should be "every God-inspired Scripture is beneficial" Some also ask whether it should be "all" Scripture or "every" Scripture.
For me and my biases, I suggest that the theme of the passage and of the whole letter is a pastoral encouragement of Timothy to preach and teach, so this particular adjective needs to be read in that context. Thus "every God-inspired Scripture" would sit most happily. I think it is possible that some are caught up in the idea that "this happened because that is what God would have done", thereby presuming what they want to prove.
Having done this, problems with "inspiration" referring to the corrupted texts that Timothy (Paul and Jesus) heard means that a new term had to be invented for the original words: "inscripturation", as well as expressions such as "verbal plenary". Layer upon layer, when the original text at 2 Timothy provides no explanation of a process. And we have such things as "adjectival verbals", and so on, without my knowing whether these were used at that time or whether the anonymous writer intended such a grammatical structure.
The variety of explanations shows the weakness of the original statement. Let me go out on a limb and suggest something even more way out: "all Scripture-inspired-of-God" or "all Scripture is inspired-of-God". Not being a scholar of Greek nor a grammarian, I am quite likely to be shot down in verbal flames.
Yes, which of the Jewish writings were available to Timothy?
Most commentators say that the word was invented at 2 Timothy, although I did locate the statement: "theopneustos (inspired by God) is rare, not being used before the Hel[lenic] period and then only with reference to divination", which I noted at page 5 of my Study. Paul (although likely not the writer of 2 Timothy) invented many ideas that are crucial to Christian mythology. Always remember that he was the earliest writer and that others copied ideas from him. (Hint: eucharist, and significance of baptism.)
As I wrote - read widely from the range of views, argue with yourself, make decisions, be prepared to keep learning and adjusting. The joy is in the hunt, in the mental gymnastics. The Bible is a very human book.
Doug