I recently posted a question here regarding a passage in Romans citing a verse in Habakkuk. My understanding is that in this and (all?) other references to Hebrew scripture Paul cites the LXX (although he changes it, here and elsewhere) rather than translating the Hebrew himself. He was clearly fluent in Aramaic (Acts 22) and I presume read Hebrew. Can we assume that he had in mind the Hebrew scripture, (and that this was similar enough to the Masoretic text we have) so that the Hebrew text is a useful source for us to understand Paul's intended meaning?
We can be sure that Paul also spoke Hebrew fluently. First up, Mishnaic Hebrew was a living language in first century Judea and well-known even among the common people. Along with that, even though modern translations use "Aramaic" when referring to the language spoken in Judea (such as there in Acts 22:2 and 21:40), the Greek reads, "...in the Hebrew language" (tae Hebraidi dialectow). There was a Greek word for Aramaic (Suristi), it was known and used by Jews (Josephus Antiquities 10:8 and many other places, Letter of Aristeas 11, and the Epilogue to Job in the Septuagint), but is never used in the New Testament. Since the ancients were capable of distinguishing the two languages (and often did), that they use the word Hebrew in Acts strongly suggests they really mean Hebrew and not Aramaic.
The event you reference in Acts shows us also that the language is Hebrew by the crowd's reaction. They became very quiet. Israelites were raised with a reverence for the Hebrew language. It was called "the tongue of Torah," "the tongue of angels," "the tongue of Heaven," and, most importantly, "the holy tongue" (Sifre to Deuteronomy 333; BT Shabbat 115a; Bava Batra 82a; Hagigah 16a, etc.; Bereshit Rabba 18:4; Kohelet Rabba 7:8, etc.).
That Paul, a Pharisee trained by Gamaliel (Acts 22:3), would not know Hebrew is unthinkable. Gamaliel was the Nasi of the Pharisees and Av bet Din of the Sanhedrin (BT Shabbat 15a). That means he was head of the Pharisees and co-chair of the Sanhedrin (with the High Priest being the other co-chair). Gamaliel was the first of only seven rabbis to be given the honorific Rabban (our teacher, meaning that he was recognized as the greatest teacher of his generation).
It is this association with Gamaliel that leads to Paul's love of the Septuagint. Like his grandfather Hillel (Soferim 16:9), Gamaliel loved the Septuagint. Gamaliel even said that Greek was the only language into which the Torah could be perfectly translated (Sotah 49b; cf. Berachot Rabbah 36:8; Devarim Rabbah 1:1; Megillah 1:8). Paul is like Gamaliel not only in his use of Greek but in how he uses it. Paul employs the same techniques of interpretation that can be seen in Hillel and Gamaliel1.
Since Gamaliel had taught Paul that the Septuagint was a good translation, and Paul's letters were written to people who spoke Greek as their primary tongue, using the Septuagint instead of translating the Hebrew himself makes perfect sense. He expects at least some of them will check it out. Therefore, he needs to use a version that they will have access to.
Even though he wrote in Greek, Paul uses Hebrew idioms. For example in Philippians 3:21, Paul uses the Hebrew Genitive, that is using an abstract noun in place of an adjective of quality. There, Paul compares "our lowly body" (literally "the body of our lowliness") to "his glorious body" (literally "the body of his glory"). Paul also uses the Hebrew idiom "son" followed by a genitive in such places as 1 Thessalonians 5:5 "people who belong to the light" (literally "sons of light"), and Colossians 1:13 "his dear son" (literally "the son of his love").
So, yes, we can conclude that Paul had in mind the Hebrew Scriptures. Assuming that it is close enough to the Masoretic for our purposes is a safe assumption (for the most part. Naturally, there are differences but textual criticism is another topic.).
1 Jeremias, J., "Paulus als Hillelit," in Neotestamentica et Semitica (E.E. Ellis and M. Wilcox, eds). Edinburgh: T. & T. Clark, 1969, pp. 88-94). See also Waverly Nunnally's article "Gamaliel" in Eerdman's Dictionary of the Bible, pp. 481-482.
Paul was probably a diaspora Jew and, if we accept the Acts account (Acts 9:11), came from the city of Tarsus. While the diaspora Jews of Babylon retained Aramaic as their first language, the Jews of the Greek-speaking world abandoned Aramaic and spoke Greek as their first language. Mark Avrum Ehrlich says (Encyclopedia of the Jewish Diaspora, page 9) that in the west - the Greek-speaking Mediterranean world - the Jews wrote and spoke only Greek. The assumption is that even a bilingual Greek-speaking person would probably think in this, his first language.
As a well educated man, Paul may have spoken other languages such as Aramaic. In this respect, it is worth noting that Philo of Alexandria, a Jewish near-contemporary, never wrote in Aramaic and does not appear to have known either Aramaic or Hebrew. Paul invariably uses the Greek Septuagint, rather than the Hebrew scriptures which very few diaspora Jews could have read.
In Acts 22:3, Paul says that he learnt at the feet of Gamaliel. Raymond E. Brown says in An Introduction to the New Testament, pages 425-6, that the claim that Paul was brought up in Jerusalem and educated by Gamaliel probably needs qualification. Paul's letters do not suggest that Paul had seen Jesus during the public ministry or at the crucifixion, and so implicitly cast doubt on Paul's continuous presence in Jerusalem in the years 26-30/33. Brown also says that because Paul shows no evidence of knowing the Hebrew scriptures, there must be considerable doubt whether he was really educated in Jerusalem, by Gamaliel or any other rabbi.
Although Acts 22:2 says that Paul spoke to the people in the Hebrew language, we have to assume that the author meant the Aramaic language, since the people would not have understood what he was saying if he spoke in Hebrew. Orville Boyd Jenkins ('Hebrew Usage in the First Century') says that the strong weight of evidence, and the prevailing opinion among both biblical and "secular" scholars seems to be that Hebrew had fallen out of general use much earlier, as a language of common, general use. He says it is likely some or all of the priestly class still spoke Hebrew in their own circles, and perhaps some of the Pharisees in Jerusalem. However, Paul was speaking to a mob, not just a few elite members of the priesthood; in danger of his life, he would have spoken in Aramaic, the one language that all the Jews in Jerusalem would understand. Thus it can not be assumed that Paul could either read or speak Hebrew. Paul's first language was Greek, so we should say that Paul must also have thought in Greek.
Fr. Brown has raised serious doubts about whether Paul was ever taught by Gamaliel and we also know that Paul only used the Septuagint for the allusions in his epistles, so the weight of evidence is that Paul had not learnt the Hebrew scriptures. If he had known the Hebrew scriptures, he must at times have used material from the LXX unconcerned that a Jew accustomed to the Hebrew scriptures would have considered those citations erroneous. His intended meaning can not be found in the Masoretic texts.