I've seen no evidence that they used the LXX. Do you have any such evidence? Most of the scrolls found at Qumran were written in Hebrew, not Aramaic, not Greek. Some were even written in Paleo Hebrew.
Only what I've read of people experts in the transmission of the New Testament, who know Biblical Greek. The New Testament more often than not uses the Septuagint. This would be obvious given that it was written in Greek and that there was a prior Greek translation of the Old Testament well in use for the Apostles to draw upon.
If you are going to suggest the quotations in the New Testament represent brand new translations on the Apostles part from the original Hebrew to Greek, that would be for you to establish. I can't read ancient Greek and therefore I have to rely on the textual critics here whom I have no reason to doubt.
It is clearly evident from manuscripts dated from that time period, that Hebrews were writing in Hebrew.
Scholars have strong evidence that Matthew was originally written in Hebrew. What evidence do you have that a letter written by a Hebrew to Hebrews was written in anything other than Hebrew, other that a copy of a copy of a copy from hundreds of years later, from a mummy?
Evangelical Textual Criticism: Early Manuscript of Hebrews Discovered
I told you this earlier. I'll repeat myself. I know of the evidence of Matthew being written originally in Hebrew (though I take it to mean Aramaic). That evidence comes from the text itself and the Church father's testimony of it so I'm not denying that of Matthew. The rest of the New Testament for the most part it is clear that it was written in Greek.
If you are going to impugn the Greek new Testament because we don't have the original autographs then you at least ought to be consistent and reject Matthew's being written in Hebrew. We don't have any Hebrew copy of that text of substantial antiquity. The earliest I believe is the Peshitta, which isn't even in Hebrew but in Aramaic. In fact he only text of the New Testament you can rely upon in general is Greek text because it is the best representation of the text. Though I've seen your creative interpretations which don't seem like interpretations but impositions of your Judaism on the text.
Other than the textual tradition it makes sense for much of the New Testament to be written in Greek because of how widely the language was used and the large geographic extent the early Church covered. When Paul wrote to the Roman community, why should we suppose the text was in Hebrew, an archaic and liturgical language when it could have been more easily read and understood in Greek? You also can't assume the New Testament was written for other Hebrews exclusively. Luke for instance was not an Apostle and wasn't even Jewish. He writes as a Greco-roman historian would and has to explain some of the Hebrew words and context to his audience whom are evidently not familiar with that sort of thing.
Since now we've established that the Septuagint was a BC production should it not be obvious that Second Temple Jews didn't have the same hang ups with writing and using Greek that you do? Greek Jewish literature existed in the writings of Philo, Demetrius and Josephus.