Who was the Author of the Piyut "asher hanee" that ends with Shoshanat Yaakov? Why is it said by Ashkenazim after they read the Meggilah at night?
This article has a writeup on the subject, speculating that it was written no later than about 500 CE (i.e., during the Talmudic era), based on its style.
Machzor Vitry in fact places it earlier, tracing it to the Anshei Knesses Hagedolah.
Still other sources attribute it to R. Asher Halevi of Worms (late 11th-early 12th century).
As for why it's said: the article cited above explains that it originally seems to have been a poetically expanded form of a berachah ending with בא"י הא-ל המושיע, and that when this berachah ceased to be said (it is combined with הנפרע לעמו ישראל מכל צריהם, as per Rav Papa in Megillah 21b), the piyut was preserved independently. (The last lines of it also fulfill the obligation, mentioned in the Yerushalmi (Megillah 3:7) and established as halachah (Shulchan Aruch, Orach Chaim 690:16), of saying ארור המן and וגם חרבונה זכור לטוב.)