Noise Source in Direct Form 2 Diagram
I suspect your f[n] deduction is correct, but the e[n] is not. Reason is that noise fed back does not behave the same way is the IIR part as in the FIR part of the filter. 

I might be mistaken here - it's been many years since I've done noise analysis. This document seems to confirm it though (even though the error seems quite small).