Q: Does C13 assume that the 9th and 11th are part of the Chord(as well as the 1,3,5,7 whatever)?
A: i'm gonna venture out on a limb and say if you see C13 written, you should probably play Bb, E, and A, and maybe D. (bass would take C). if they wanted F#, they should have told you so. if they want F, they should say sus4 and you should NOT play E in that case. that's just my experience from out in the world or whatever