1)

THE DESCENDANTS OF HILLEL

כדתניא לא יסור שבט מיהודה אלו ראשי גליות שבבבל שרודין את ישראל בשבט ומחוקק מבין רגליו אלו בני בניו של הלל שמלמדין תורה ברבים
Translation: As it is taught in a Baraisa: 'The scepter will not depart from Yehuda,' (Bereishis 49:10) these are the Reish Galusas of Bavel, who rule over the Jews with a stick (The Reish Galusa was authorized by the Babylonian government to administer justice.). 'Or the legislator from between his feet,' (ibid) these are descendants of Hillel (the Nasis in Eretz Yisrael) who teach the Torah in public (but have no governmental authority).
(a)

Why does the Gemara mention 'the descendants of Hillel' but not Hillel himself?

1.

Ben Yehoyada: That phrase refers specifically to Rebbi Yehuda haNasi, who taught Torah to very many students. In fact, his position as redactor of the Mishnah makes him the teacher of all of Klal Yisrael for all of the generations after him.

5b----------------------------------------5b

2)

THE FAMILY OF R. CHIYA

מ״ש למר דקא קרי בן אחי ומ״ש למר דקא קרי בן אחותי וכי תימא הכי הוה מעשה והאמר מר איבו וחנה ושילא ומרתא ורבי חייא כולהו בני אבא בר אחא כרסלא מכפרי הוו רב בר אחוה דהוה בר אחתיה רבה בר חנה בר אחוה דלאו בר אחתיה ואי בעית אימא על שם חכמתו דכתיב אמור לחכמה אחותי את
Translation: Why did Master (R. Chiya) call Rabbah bar Chanah my brother's son, and why did Master call Rav my sister's son? And if you will say that is how it was (that Rav was his sister's son, not his brother's son), but the Master said: Aivu (Rav's father) and Chanah (Rabbah's father) and Shila, and Marsa, and R. Chiya were all sons of Abba bar Acha Carsela of Cafri (in Bavel)? (Therefore, Rav was R. Chiya's brother's son.) Rav was the son of R. Chiya's brother (his father's son from a different mother) and he was also the son of R. Chiya's sister (his mother's daughter from a different father), while Rabbah bar Chanah was the son of R. Chiya's brother, but not the son of his sister. Or, if you want, say that it was on account of his wisdom, as it is written (Mishlei 7:4): 'Say to wisdom, you are my sister.'
(a)

Here, Shlomo haMelech is referring to the Torah as a sister. Why elsewhere (Mishlei 31:10), does he refer to it as a wife ('Eshes Chayil Mi Yimtza')?

1.

Ahavas Shalom (Likutim): Each of these types of love has an advantage over the other. The nature of a person is to love his wife more than his sister. But the love of a sister is uninterrupted from the beginning to the end of his life. A person's love of the Torah should have both of these aspects.