There are several different things that you are touching on in this question.
Avram was sent an angel when he was three years old who taught him Torah directly while he lived in a cave, hidden from the world. King Nimrod, based on the recommendation of his Astrologers, wanted to murder the so to be born son of Terach. To avoid his newborn son being discovered by King Nimrod, Terach sent his wife, Amatlaye, the daughter of Kerenebo (An allusion to the Essence of Har Nebo, the place from which Moshe Rabbeinu, in the future, would gaze in order to see the land of Israel.) , her nursemaid and the newborn Avram into hiding. The details of this story are found in Sefer HaYashar, parshat Noach 8-11.
Like with Adam following the sin of the Tree of Knowledge of Good and Evil, G-d sent the angel Raziel רזיאל (A name meaning Secret of G-d, alluding to the secret of Reward and Punishment. That the reward for the negative precepts is spiritual reward pertaining to the World of Souls and the reward for the positive precepts, which pertain to the material, physical body, is the bodily reward of resurrection.) to teach Avram the whole Torah directly.
That originally the revealed aspect of Torah, meaning what people must adhere to, was only about the negative precepts, the prohibitions. Do not transgress and violate these prohibited things. The concealed or inner aspect of the Torah related to the positive precepts. This is hinted at through the gematria of the angel's name which is 248 corresponding to the 248 positive commandments which correspond to the 248 limbs of the male body.
All of these 248 positive commandments can be learned from the text of the written Torah when applying all the rules of grammar. (Grammar in the broadest sense meaning all aspects of Crowns, Trop, Nekudot, and Letters, Notarikon, Gematria and all the letter transformations.) That specifically, the ten utterances in Bereshit correspond to the ten commandments that were given at Mount Sinai. And encoded within the ten commandments (and also the ten utterances) are all of the negative and positive precepts.
And it is in this sense that so too, when Avraham had mastered all aspects of the 248 positive precepts of the Torah (his ten trials), that his name was changed from Avram אברם to Avraham אברהם, which is also gematria 248. The symbol of his completion and mastery was the first positive precept of the covenant of Milah (circumcision).
The next detail you are asking about is the idea of Avraham's relationship to the 7 commandments of Noach in contrast to the 613 commandments of the Torah. The general concept is like is mentioned above, the commandments of Noach are all expressed as negative precepts, prohibitions. The revelation of the positive precepts began with the positive commandment of Milah. But Avraham and the the other Patriarchs and Matriarchs performed the other positive precepts on a spiritual level. From the descriptions within the Torah and associated midrashim, this appears to be related primarily to the Kavanot, the intentions related to particular acts or events.
For example the discussion of Yaacov Avinu and the sticks with the sheep of Lavan at the watering trough. The actions with the sticks pertained to the precepts of Tefillin. But because they were only on the level of the intentions, the sticks used by Yaacov retained no aspect of Holiness קדושה afterward, unlike with actual Tefillin.
There is also discussion of where, geographically, the Patriarchs and Matriarchs were at specific times. That while in the Land of Israel, they were focused on the spiritual intentions. But outside the land of israel, under the dominion of those influences, they focused on adherence to the revealed aspect of the precepts for that time, meaning the commandments of Noach.
The third detail you touch on is whether and when Avram went to and attended the Yeshivah of Shem and Ever.
This occurred when Avram was ten years old, when he, his mother and his nursemaid finally departed from hiding in the cave. They went from there to the household of Noach, where Shem lived in order to study Torah as it had been transmitted to Adam from the angel Raziel, to his son Seth and his decendents until Noach and his son Shem.
This too is detailed in Sefer Yashar, parshat Noach, 12.
