How did R. Abba bar Zavda deduce from the Pasuk that even though a Jew has sinned, he is still called a Yisrael?

Poras Yosef: The Pasuk (Yehoshua 7:11) does not say 'ישראל חטא', but rather, 'חטא ישראל' - he is still called a Yisrael after the sin.

Metzudas David (Yehoshua 7:11): (R. Abba bar Zavda's teaching should be understood totally differently, and it should be read as follows...) - 'Af Al Pi Shechata' - 'Although only an individual sinned'; 'Yisrael Hu' - 'it is (all of) Yisrael' - the Pasuk attributes the sin to all of Yisrael, because they are held responsible for one another.

Why do Chazal describe Achan's sin as equivalent to transgressing all Five Books of the Torah?

Iyun Yaakov: Since he transgressed the Five Books of the Torah, which correspond to the four death penalties of Beis Din together with death from Heaven, he was therefore punished with the most severe form of capital punishment, namely Sekilah (stoning).

Maharal: He committed a single sin that is considered equivalent to transgressing the entire Torah.

Maharsha: He transgressed most of the Mitzvos that are written in the Five Books of the Torah.

Yad Ramah: The phrases of the Pasuk (Yehoshua 7:11) that describe Achan's five sins are each written in a different Book of the Torah. "They have also transgressed My covenant" corresponds to (Bereishis 17:14) 'one who does not circumcise he has broken My covenant'. "They have also taken of the consecrated thing" corresponds to (Vayikra 27:28), 'all devoted things are holy of holies to Hashem'. "And they have also stolen" corresponds to (Shemos 20:13), 'Do not steal'. "And also acted deceitfully" corresponds to (Bamidbar 5:7) referring to one who takes a false oath and denies that he who stole from a convert, 'and he shall make restitution for his guilt in full'. "And they have also put into their vessels" corresponds to (Devarim 23:25), 'but you shall not put (any) into your vessel.'.

Kli Yakar (Yehoshua 7:21): He transgressed the prohibition of theft that appears in all Five Books of the Torah. In Bereishis (2:16), Adam was told that he may eat from all of the trees of the Garden and the Gemara later (56b) expounds that he was warned not to steal. In Shemos (20:12), it is written 'Do not steal'. In Vayikra (1:2) in discussing the Korbanos, it teaches 'If a man from you sacrifices' - this forbids bringing from stolen animals. In Bamidbar (15:38), the Pasuk states 'And you shall make for yourselves Tzitzis, which the Gemara (Succah 9a) expounds 'but not from stolen items'. In Devarim (5:16), it again states 'Do not steal'.

Sefer Chasidim (Siman 106): Anyone who benefits from such banned property, it is as if he has transgressed the entire Torah, since if one calculates the numerical value of the first and last letters of the last word of each of the Five Books of the Torah, it totals 248, which is the same as the word ' חרם - Cherem' - banned. (Bereishis ends with the word 'במצרים' - 'ב' & 'מ' = 42. Shemos ends with 'מסעיהם' - 'מ' & 'מ' = 80; Vayikra ends with 'סיני' - 'ס' & 'י' = 70; Bamidbar ends with 'יריחו' - 'י' & 'ו' = 16; Devarim ends with 'ישראל' - 'י' & 'ל' = 40. 42+80+70+16+40 = 248.)

What is behind the disagreement between R. Yehudah and R. Nechemiah regarding the 36 that were killed?

Iyun Yaakov, Sanhedri Ketana: It is a result of their earlier disagreement (end of 43b) regarding collective responsibility ('Arvus') for the sins of an individual. R. Yehuda held that Am Yisrael had already accepted it (i.e. 'Arvus') even for hidden sins. Consequently, not only the leaders, but all of Yisrael bore responsibility for Achan's sins. As a result, 36 people were killed. R. Nechemiah held that Arvus was only accepted for revealed sins, but not for hidden ones. Although the sin of Achan was considered revealed, as his wife and children were aware of it, the primary responsibility rested with the leaders and the Sanhedrin to expose the sins and protest them. Consequently, R. Nechemiah understands the Pasuk as referring not to 36 individuals who were killed, but to a single leader among them, Yair, who was considered equal in stature to 36 members of the Sanhedrin.

Aruch laNer: It is a result of (another aspect of) their earlier disagreement, namely, about punishment for revealed sins before they crossed the Jordan. R. Yehudah held that they were punishable. Hence there were three covenants in this matter - at Sinai, in the plains of Moav and at Har Grizim. Therefore, 36 people died, as there were 12 tribes and three died from each tribe, corresponding to the three covenants. But R. Nechemiah held that there were no covenants on the hidden sins, which removes the basis for 36 people to die. Hence, he concluded that only one person actually died.

Why was Moshe referred to as poor and Yehoshua as rich?

Maharsha: Moshe was not given permission to conquer the Land, while Yehoshua was.

R. Yoshiyahu Pinto (Rif): Moshe was not permitted to enter the Land, while Yehoshua was.

Iyun Yaakov: Moshe was close to the time of his death and it states (Koheles 5:14), "As he left his mother's womb, naked shall he return to go as he came" - a person approaching death is considered 'naked' and thus 'poor'. Yehoshua, by contrast, still had many years ahead of him and was therefore considered 'rich'. (Seder Olam Rabbah states in Perek 12, that Yehoshua led the nation for 28 years.)

What is the meaning of 'he lodged in the depth of Halachah'?

Toras Chaim: Certainly, Yehoshua was learning Torah even at the time when the angel came. However, since he was in the midst of sieging the city of Yericho, he was not learning 'B'Iyun' (deeply) but rather, more superficially. The angel came to instruct him that there is a charge against him that he did not learn properly. Therefore, in the battle is Ai he corrected this and learned in depth.

Is there any dispute between R. Elazar, Reish Lakish and R. Yochanan?

Mishnas Yosef: The Maharsha and the Ben Yehoyada imply that there is no dispute; rather, each statement builds upon the previous one. R. Elazar teaches that one should pray before trouble comes, since once it has arrived it is a time of Divine judgment, and salvation is more difficult. Reish Lakish adds that if one prays with maximal effort and concentration, especially if one fasts, then the prosecuting forces on High cannot interfere, and his prayer passes straight between them to the Divine Throne. R. Yochanan then adds that, in addition to praying with great effort, a person should ask Hash-m to ensure that he does not have enemies on High, and instead that Angels of Mercy assist his prayers in ascending before Hash-m.

How do we know that it was Achan's confession that atoned rather than his death? (Maharsha)

Maharsha: The Pasuk seems to indicate this, since death had not yet been mentioned at this point. According to the opinion stated later (47b) that for those executed by Beis Din, death does not atone until the flesh has decomposed; in this case, however, Achan's confession with his death effected atonement (immediately without the need for decomposition).

Aruch laNer: Since in Achan's case, it was death with confession, we can only learn from here that death with confession atones.