Understanding G-d's name of essence and relationship with our forefathers

(2) God spoke to Moses and said to him, “I am the HaShem. (3) I appeared to Abraham, Isaac, and Jacob as El Shaddai, but I did not make Myself known to them by My name HaShem (יהוה).

The intent in the name El Shaddai is the one who sustains and feeds everything. Through the name of Shaddai, HaShem gives sustenance and blessings to all His creations, similar to the word shadayim (breasts) that are prepared to provide sustenance to the child...and the intent in the name YHVH is that he is a master of all the worlds and there's nothing stopping him from doing anything He'd like in the world. He can change the laws of nature or remove them completely...Now behold, He gave the forefathers wealth and honor and all temporary good things, he saved them from death and war, from the name of Shakkai, however he didn't interact with them in a supernatural and wonderous way (as the Ramban writes that HaShem adjusted the nature of the world for our forefathers within the natural functions in a way that it didn't override scientific laws).

Rav Hai said in the High Priest's viduy (confession) he would use the 42 letter name of G-d and it's still found in the yeshivas of kabbalah and known to the wise men. But that does not appear correct to me, rather it's referring to the 4 letter name, and that's what we refer to as the "shem hamefurash," the explicit name. This name is the source of all other names, as all other names extend from it...

I've heard in the name of the Ba'al Shem Tov to explain the verse, (Psalms 17:15) "In justice I will see your face" meaning when a man gives charity to a needy person he is doing a "yichud" (act of G-dly unity), as the coin represents the yud of G-d's name, the hand of the giver represents the Heh of G-d's name, the extension from giver to recipient is represented by the vav of G-d's name and the receiver's hand is represented the final heh in G-d's name...