I know that Purim does not halt Shiva the way the Shlosh Regolim and rosh HaShonna and yom Kippur do, but does one sit shiva on Purim. Does one go to Shul to listen to the Megilah, and sit on a regular seat?

There are no Minhagim of Avelut on Purim! On both days one is allowed to go to shul, read the Megilla and sit on a regular seat. This Halacha is relevant even if one lives in a place where only one day of Purim is kept - only the fourteenth of Adar or the fifteenth. This is the Psak of the Rm"a in Orach Chayim 696:4. There are Poskim who disagree with him. Happy Purim Rabbi Zalman Baruch Melamed