What exactly was the 'Eishel' that Avraham built and what purpose did it serve?
Rashi #1: An orchard which provided fruit for his many guests.
Rashbam: He planted an orchard in order to Daven there. Rashi (in Avodah-Zarah 7b) and Targum Onkelos: A tree next to which he Davened.
Lev Eliyahu (Bereishis p.41): He made it after Shem told him that they left the ark in the merit of Tzedakah that they did with the animals. Avraham reasoned that all the more so, one should do so with people!
Rashi (in Sotah 10a): Eishel", is the acronym of 'Achilah, Shesiyah, Leviyah' (eating, drinking and escorting). Kol Eliyahu - Avraham wanted to fix the Chata'im of Adam (eating), Noach (drinking) and S'dom (Levayah).
What does the Pasuk mean when it writes "Vayikra Sham be'Shem Hashem Keil Olam"?
Rashi and Targum Yonasan: As a result of his Chesed activities, Hashem's Name became known in the world - When his guests had finished eating and drinking, he would ask them to bless their benefactor. 1
Seforno and Ramban #1: He would inform them that Hashem is the G-d of time and that He constantly recreates it. 2
Ramban #2: He taught them that Hashem is in full control of the entire world (both Heaven and earth).
Ramban #3 (citing the Moreh Nevuchim): He taught them that Hashem preceded the beginning of time.
Targum Onkelos: It means simply that he Davened there to Hashem, the G-d of the world.
Rashi said that the Eshel was for Avraham's guests. Surely he had many guests over many years. Why is the Torah so concise about this, and writes an entire Parshah for the Akeidah?
He adds that the Torah elaborates about hosting the angels, to teach that the intent is primary. There, the action was nothing, for they did not need to eat!
This is not in every respect. It is harder to do Teshuvah for Mitzvos Bein Adam l'Chavero, for one needs also pardon of the afflicted party. Some say that engaging in a Mitzvah Bein Adam l'Makom does not exempt from Mitzvos Bein Adam l'Chavero (in Yabi'a Omer 9:84). The Torah elaborates about episodes from which we learn Midos and Derech Eretz more than about Mitzvos Bein Adam l'Makom (refer to 24:42:3:1)!