What song is playing 12 minutes into episode 13 of Code Geass R1?
The song is titled Stories, sung by Hitomi Kuroishi (黒石ひとみ). 

More details about it is here:
http://codegeass.wikia.com/wiki/Stories

Here is the youtube link:
https://www.youtube.com/watch?v=PN0fkr2XoCM