For comparison, here is a selection of the citations in full from the excerpt above:
1. study for its own sake
(NOTE: From my reading of the extant texts, Epicurus does not advocate study "for its own sake." One studies the texts and nature to alleviate ignorance, fear, anxiety about death and gods, etc. There is always a practical application of study. For example: "Hence, since such a course is of service to all who take up natural science, I, who devote to the subject my continuous energy and reap the calm enjoyment of a life like this" (Epicurus, Letter to Herodotus)
Vatican fragment 45
The study of what is natural produces not braggarts nor windbags nor those who show off the culture that most people fight about, but those who are fearless and self-reliant and who value their own good qualities rather than the good things that have come to them from external circumstances.
Avot 6:1
The sages taught in the language of the Mishnah. Blessed be He who chose them and their teaching. Rabbi Meir said: Whoever occupies himself with the Torah for its own sake, merits many things; not only that but he is worth the whole world. He is called beloved friend; one that loves God; one that loves humankind; one that gladdens God; one that gladdens humankind. And the Torah clothes him in humility and reverence, and equips him to be righteous, pious, upright and trustworthy; it keeps him far from sin, and brings him near to merit. And people benefit from his counsel, sound knowledge, understanding and strength, as it is said, “Counsel is mine and sound wisdom; I am understanding, strength is mine” (Proverbs 8:14). And it bestows upon him royalty, dominion, and acuteness in judgment. To him are revealed the secrets of the Torah, and he is made as an ever-flowing spring, and like a stream that never ceases. And he becomes modest, long-suffering and forgiving of insult. And it magnifies him and exalts him over everything.
2. acquisition of a companion
Letter To Menoeceus, end
Meditate day and night then on this and similar things by yourself as well as together with those like yourself.
Avot 1:6
Yose ben Yochanan (a man) of Jerusalem used to say: Let thy house be wide open, and let the poor be members of thy household. Engage not in too much conversation with women. They said this with regard to one’s own wife, how much more [does the rule apply] with regard to another man’s wife. From here the Sages said: as long as a man engages in too much conversation with women, he causes evil to himself, he neglects the study of the Torah, and in the end he will inherit gehinnom.
3. diet of bread and water
Bailey, fr. 37
I am thrilled with pleasure in the body, when I live on bread and water, and I spit upon luxurious pleasures not for their own sake, but because of the inconveniences that follow them.
(NOTE: I've also addressed the "bread and water" issue in my translation to the letter to Menoikeus. Epicurus doesn't call us to have a life of "privation"... See Avot 6:4 below)
Avot 6:4
Such is the way [of a life] of Torah: you shall eat bread with salt, and rationed water shall you drink; you shall sleep on the ground, your life will be one of privation, and in Torah shall you labor. If you do this, “Happy shall you be and it shall be good for you” (Psalms 128:2): “Happy shall you be” in this world, “and it shall be good for you” in the world to come.
4. avoidance of public office
NOTE: We're fairly familiar with the "avoidance of public office" trope in current and former discussions here on the forum. A number of papers shared here have called that idea into question with respect to the ancient Epicureans.
Avot 1:10-11
Shimon ben Shetach used to say: be thorough in the interrogation of witnesses, and be careful with your words, lest from them they learn to lie.
Shemaiah and Abtalion received [the oral tradition] from them. Shemaiah used to say: love work, hate acting the superior, and do not attempt to draw near to the ruling authority.
Those four will do to illustrate my point. The citations have the most superficial similarities. The Epicurean "bread and water" sentiment especially has nothing to do with the living a life of privation. They could all be the result of convergent evolution. The statement "Agreements, however, both in content and literary form, between rabbinism and Epicureanism" does not deliver on its claim to be "striking." Your assertion that the Jewish movements (which it appears you're including Christianity under that name) copied aspects of Epicurus's philosophy doesn't seem to be substantiated by what I've seen
Are we in agreement that (1) Epicureanism was the first major cult that spread its message chiefly though the medium of epistolography and (2) the first major school that envisioned a community of equals and friends without the mediations of poltical authority?
Unfortunately, I don't think we're in agreement on those two points. "Spreading its message chiefly through the medium of epistolography" doesn't strike me as quite accurate. One issue is that Epicurus had to communicate with his far-flung communities by letter during his lifetime. That was the means of communication, both for him and for Paul. They used similar media in similar circumstances. That doesn't mean Paul was inspired by Epicurus. I'm not sure how many letters we have from Epicurus's successors. It seems from the lists and extant texts, especially from Philodemus, that the Epicureans were much more interested in writing treatises than letters. Epicurus seems to have written as many treatises/books as letters, especially considering On Nature is 37 books itself.
On point 2, I'm not sure what you mean by "without the mediations of poltical authority." I wanted to also ask when you refer to the "community of equals and friends" are you referring to Epicurus's inclusion of women and enslaved people in his community, or the relative equality of students (of all kinds) in the Garden? Because I get from some of the texts that there was a definite hierarchy of teachers and students within the Garden for purposes of Epicurean education while they also thought of themselves as friends in time of need (and at other times as well).
I agree that Epicureanism was a potent, vital, active school of philosophy in the ancient world with communities from France (Gaul) to as far away as the area of modern Turkey in Oenoanda. But I maintain that similar strategies does not require inspiration or copying. Superficial similarities can simply be that religions and philosophies came up with similar solutions to similar problems.