There is a current academic attempt (by Prof. Moshe Tzipor from the Bar Ilan University) to reconstruct the original Hebrew text the Greek translation was based on. It has extensive notes, comments and explanations. As far as I can tell, only the first volume (Bereshit/Genesis) has been published so far:
Aside from the Talmud, the story of the Septuagint is mentioned in the minor tractate Soferim (1:7-8):
מעשה בה׳ זקנים שכתבו לתלמי המלך את התורה יונית והיה היום קשה לישראל כיום שנעשה העגל שלא היתה התורה יכולה להתרגם כל צרכה:
It once happened that five elders wrote the Torah for King Ptolemy in
Greek, and that day was as ominous for Israel as the day on which ...
To the title question, “Is there still a mesora on how to write the Torah in Greek?”:
The Rambam in Mishneh Torah writes that Greek language has been forgotten.
Laws of Tefillin, Mezuzah and Sefer Torah - Chapter One Halacha 19
Tefillin and mezuzot may be written only in Assyrian script.
Permission was granted to write Torah scrolls in Greek as ...
Nearly all of Philo's writings are explanations of the Septuagint version of the Pentateuch, though I believe the only ones that actually go through the books in order as a commentary are his Questions and Answers on Genesis (at the above link) and Questions and Answers on Exodus.
Other Jewish authors who used the Septuagint, such as Artapanus, Ezekiel and ...
R. Hayim Heller wrote a sefer on the Septuagint. I'm not sure if you would quite call it a commentary, but you can access the sefer here. I think he also wrote something on it in German, called Untersuchungen zur Septuaginta. As described in his profile page on YUTorah:
A gaon in Mikra, he published the Targum HaPshitah on Bereishit and
Shemot and a ...
Interestingly, the Steinsaltz Gemara on this segment comments
The seventy-two Elders, in their translation of the word hare in the
list of non-kosher animals, used the word δασύπους, dasupous, which
literally means hairy-legged or roughfooted, instead of the standard
term for hare, λαγός, lagos. They did so because the nickname of the
founder of the ...
In Shmuel 1 17:4 it writes:
וַיֵּצֵ֤א אִֽישׁ־הַבֵּנַ֙יִם֙ מִמַּחֲנ֣וֹת פְּלִשְׁתִּ֔ים גָּלְיָ֥ת שְׁמ֖וֹ מִגַּ֑ת גָּבְה֕וֹ שֵׁ֥שׁ אַמּ֖וֹת וָזָֽרֶת׃
A champion of the Philistine forces stepped forward; his name was Goliath of Gath, and he was six cubits and a span tall. (sefaria translation)
The Midrash Aggadah Devarim 3:11 qualifies אִֽישׁ־הַבֵּנַ֙יִם֙ in ...
Midrash Tehillim 18:32 (cited in Rashi, I Shmuel 17:49) says that Goliath fell forward after David struck him with a stone (rather than, as might have been expected, backwards)
כדי שלא יצטער דוד וילך ויחתוך את ראשו. נשתכר י"ב אמה וזרתיים
so that David wouldn't have to go to so much trouble to cut off his head. He gained twelve cubits and two spans
The specific type of Greek was not known to Jews anymore, and the text became corrupted. Originally, it was felt that the Koine translation of the Torah, and specifically only the Torah, was good enough. The Greek words had specific connotations and the translation was good enough for the majority of people to get all the different layers of understanding ...
Both textual traditions (along with the Samaritan Pentateuch, which has similarities with each) predate Christianity by centuries. Basically, texts, whether religious, or otherwise, present a rainbow-like distribution in terms of variation.
To illustrate this by way of a basic example, for the purpose of clarification:
The difference in genealogies:
The late Harry M. Orlinsky was an expert on the LXX. While he wrote no commentary on the whole translation, he did publish important articles on it. A Google search ('Harry Orlinsky on the Septuagint') will reveal his work in this field. He earned his doctorate from Dropsie College for his work on the translation of Job in the Septuagint. He also studied ...
Adding to @Aryeh's answer, Josephus wrote that the name of the High Priest at the time of the translation was Elazar (Antiquities XII:2:4-7):
"Now when this had been done after so magnificent a manner, according to the king's inclinations, he gave order to Demetrius to give him in writing his sentiments concerning the transcribing of the Jewish books; ...
The original Septuagint, translated by rabbis more than 22 centuries ago, was of the Pentateuch alone, and not the Books of the Prophets, such as Isaiah.
The Talmud states this explicitly in Tractate Megillah (9a).
Josephus as well, in his preface to Antiquities of the Jews, affirms that the Septuagint was a translation only of the Law of Moses.
This is ...