What are the connotations of the phrase "Vehisvadu es Chatosam"?
Rashi (in Shavu'os, 13a): It teaches us that Chata'os and Ashamos only atone if the sinner did Teshuvah. 1
Seifer ha'Chinuch: It is a Mitzvas Asei to confess one's sins and to do Teshuvah on them. 2
Sifri: It teaches us that someone who brings an Asham must confess, just like someone who brings a Chatas.
R. Nasan (in Bamidbar Rabah, Sifri, and Yalkut Shimoni): It teaches us that someone who is about to die must recite Viduy. 3
And the Mitzvah of Teshuvah is to confess one's sin. See Rambam.HIlchos Teshuvah, 1:1.
At any time, but specifically on Yom Kipur. See Seifer ha'Chinuch, Mitzvah 364.
See Torah Temimah, note 19 and Ba'al ha'Turim. Eitz Yosef: Even at the time of death, one must confess. Vilna Gaon (on the Sifri): The text reads 'all who are executed' and we expound "ve'Ashmah ha'Nefesh" to include all Chayvei Misah. Zayis Rana'an - one must confess for every sin, therefore all who are executed confess, only others are not obligated to confess in public.
Why does the Pasuk switch from the plural "Vehisvadu es Chatasam" to the singulat "Veheishiv es ha'Gezeilah"?
Oznayim la'Torah: Because the Torah incorporates a case where someone swears falsely over a deposit or over a loan, in which case the owner is parially to blame for dealing with a dishonest person 1 and is therefore also required to do Teshuvah. Needless to say, he is not included in "Veheishiv es ha'Gezeilah", which applies to the 'sinner exclusively. 2
What is the meaning of "Ashamo be'Rosho"?
Rashi and Rashbam: It means 'the principal' (on which he swore - Rashi). 1
Bava Kama, 109a: It implies that the Pasuk is speaking about Gezel ha'Ger, where there is only the principle to pay and not about Geneivas ha'Ger, where there is also Kefel (double). 2
Why does the Torah here write "Vachamishiso" (in the singular, and in Vayikra, 5:24 - in connectioin with the same Korban Asham Gezelilos ? "Vachamishisav" (in the plural)?
Oznayim la'Torah": Refer to 5:24:2:1 and note. Because here, since the money is given to the current Mishmar of Kohanim, there there is no cpacific claimant and it is no possible to arrive at a situatiion where the Gazlan swears on the Chomesh.
What are the implications of "Venasan la'asher Asham lo"?
Rashi: It implies that he repays the money (not necessarily to the person from whom he stole, but) to the person to whom the money is owed ('Shibuda de'R. Nasan'). 1
If, for example, Reuven stole from Shimon, who owes money to Levi, Reuven must return the money to Levi. See Torah Temimah, note 20. And the Torah inserts it here, and not in Vayikra - by someone who steals from a Yisrael - to teach the Gazlan that, even though he is not giving the money to the Kohanim of that Mishmar, he obtains his full Kaparah by giving it to the Ger's creditor. See Oznayim la'Torah and Torah Temimah, note 20.