What are "bi'Zmaneihem"?
Torah Temimah citing Megilah 2a: The Megilah is read on the 11th, 12th, 13th, 14th or 15th of Adar. Bi'Zmaneihem teaches that many days were enacted. We cannot include after the 15th, for it says "v'Lo Ya'avor" (do not pass over the time for reading).
What is the meaning of "Ka'asher Kiyam"?
Vilna Gaon: It is like Mordechai commanded them.
What does "Ka'asher Kiyemu Al Nafsham v'Al Zar'am" add?
Vilna Gaon: Also Mordechai and Esther accepted on themselves and on their seed. So Mordechai commanded all of Yisrael.
Malbim: Esther explained that Bal Tosif applies only to a new matter that will be considered like Torah law. Here, they merely accept like Mordechai and Esther commanded them, like a vow.
Did they accept fasts and screams?!
Ibn Ezra: Yisrael accepted to rejoice on Purim, just like they accepted to fast on days of their mourning (the 17th of Tamuz, Tish'ah b'Av...)
Ibn Ezra citing others, Ra'avad, Rosh (Megilah 1:1 citing R. Tam): This is a support for Ta'anis Esther 1 .
Vilna Gaon: No. Just like they accepted fasts and screaming when they were in affliction, so now they accepted the Megilah.
Malbim: This supports Esther's claim that they are not accepting the Megilah like Torah law, rather, like Yisrael accepted the four fasts - "Tzom ha'Revi'i v'Tzom ha'Chamishi v'Tzom ha'Shevi'i v'Tzom ha'Asiri" (Zecharyah 8:19, i.e. the 17th of Tamuz, Tish'ah b'Av, Tzom Gedalyah and 10th of Tamur) Also they were an addition to Torah law, and all of Yisrael accepted them. This shows that one may accept new matters as a vow 2 .