Why does it say "Lachen"?
Rashi: It is an expression of a Shevu'ah. Even though you betrayed Me, I have a Shevu'ah to redeem you.
When will these days come?
Radak: They will be in the future. Hashem sends through His Nevi'im [tidings of] punishments and consolation, lest they say 'our hope is lost.' Even though I will pay them for their evil deeds, at the end of days there is hope for them.
Will we cease to mention Yetzi'as Mitzrayim?
Rashi, citing Chachamim, Brachos 12b: No. Rather, the final redemption will be primary, and Yetzi'as Mitzrayim will be secondary to it.
Radak: When one swears, he says Chai Hashem. People normally put next to mention of Hashem one of His deeds or wonders, like Tzidkiyah said "Chai Hashem Asher Asah Lanu Es ha'Nefesh ha'Zos" (38:16). People used to say Chai Hashem Asher He'elah Es Bnei Yisrael me'Eretz Mitzrayim. In the future, they will say instead Chai Hashem Asher He'elah [from the north
