Do we still have a mesora for the translation of the Torah into Greek, and if so, is this the LXX/Septuagint commonly used by Gentiles? Do we still have a mesorah for any other seforim into Greek?
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 well. That Greek language has, however, been forgotten from the world. It has been confused and has sunk into oblivion. Therefore, at present, all three sacred articles may be written using Assyrian script alone.
So we do not have a mesora on how to write the Torah or “any other seforim” in Greek.
You ask in the text, “is this the LXX/Septuagint commonly used by Gentiles?”.
A Wikipedia article writes about the past use of the LXX. It is not commonly used now.