What is "Takfo u'Gevuraso"?
Vilna Gaon: Tokef is that all heeded what he said and does it. Gibor is stronger than his colleagues, but they do not do his word. Therefore, it says "Ma'ase" next to Takfo.
Malbim: It is Achashverosh's power via Mordechai's conduct.
Why does it say that "Parashas Gedulas Mordechai" is "written in the chronicles of Madai u'Faras"?
Vilna Gaon: The Megilah only gives the Kelalim of his grandeur. The details are written in the chronicles.
Here it says Madai u'Faras. Above (1:3), it says "Paras u'Madai"!
Torah Temimah citing Megilah 12a: Paras and Madai agreed that if the kings will be from Paras, the officers will be from Madai, and vice versa.
Vilna Gaon: Achashverosh was from Paras, therefore Paras is first in the Megilah, for the king was from Paras. Below discusses the chronicles, which were earlier, from the time of Melech Daryavesh Mada'ah, so Madai is first.