I've been playing through Borderlands again, trying to complete all the missions. Occasionally, I've unlocked challenges in the game like "Not Really a People Person" (Kill 250 Humans). Some of these challenges are quite time-consuming and since I have yet to complete "Mad Moxxi's Underdome Riot", I was wondering, do kills and other actions in the underdome count towards challenges?
Yes, they do count. I've completed a human kills challenge in a Riot Arena. The Borderlands Wiki article on this DLC has this to say (emphasis added):