I played HL2: Episode 2 for about an hour but no steam trading card dropped. Do I have to play the base HL2 to get cards or are they also dropping in Episode 2?
The Steam Trading Cards beta is currently limited to Counter-Strike: Global Offensive, Team Fortress 2, Dota 2, Portal 2, Half-Life 2 and Don't Starve.
That means you'll have to play the base HL2 to earn trading cards, at least until HL2E2 is added to the list of participating games. (Half-Life 2 and its episodes are all independent games as far as Steam is concerned.)