(a) Your question, why is it called "Machpeilah" (the "cave of the double pairs" buried there) before anyone was buried there, is a good one. There are several answers:

(1) We find that the Torah often calls something by a name which refers to an event which will happen in the future (see Kesubos 8b and Yoma 6a)

(2) There was already one pair buried there (Adam and Chavah).

(3) See Insights 53:3, where we mention the view of the Ramban, who points out that Machpeilah was the name of the area in which the cave was located (and not just the name of the cave). The Gemara is just explaining why the Torah had to mention its name.

(b) The MAHARSHA explains that the point is to show the extent of the miracle which occurred for the students, enabling so many to be in such a small area. He does not explain what siginificance the numbers 4 and 6 have.

Perhaps we can suggest the following explanation. The Gemara (Chagigah 13b) says that after the destruction of the Beis ha'Mikdash, the number of wings of the Chayos were diminished from being "six, six" (that is, each one had six wings) to being "four, four," as a result of the decreased manifestation in this world of the Divine presence. In the times of Rebbi (who lived but shortly after the Churban), the students still merited to have a profound revelation into the secrets of the Torah (symbolized by "6 X 6"). But in the times of Rebbi Oshaya, although it was but a short while after Rebbi, the level of the students had diminished, and the level of Divine revelation in this world along with it.

(c) See the RAMBAM (Hilchos Talmud Torah 1:8), who writes that even one who is undergoing great physical affliction can (and is obligated to) learn Torah. Learning Torah requires only that the mind (and Neshamah) be well, and indeed, even when the body is smitten with the worst of afflictions, the mind might still be well and able to learn.

(d) The order mentioned in the Gemara is the order of the transmission of the Mitzvos to the Jewish people, when each one was given to Moshe at Sinai. The order mentioned in Avos is the order of the transmission of all parts of the Torah to the leaders of the Jewish people, from generation to generation. (The RAMBAM, in his introduction to the Mishnah Torah, indeed mentions that "Elazar, Pinchas, and Yehoshua all received from Moshe," but he adds that "to Yehoshua, he gave the Torah she'Ba'al Peh, and commanded him regarding it," meaning that Yehoshua was commanded to see to it that the Torah she'Ba'al Peh was transmitted to forthcoming generations, whereas Elazar and Pinchas were not made responsible for transmitting it to future generations.

The children of Moshe were not included in either transmission, because it was Yehoshua who was chosen to be the "heir" of the tradition from Moshe. The children of Moshe learned the Torah like the rest of the Jewish people did (perhaps they were too young at the time of the giving of the Torah, as we find that one of Moshe's sons was born and circumsized when Moshe returned to Egypt from the house of Yisro, only a year before the giving of the Torah.)

We hope you find this helpful. Be well,

-Mordecai