334.15(B) - "The cable (NM) shall be protected from physical damage where necessary by conduit..." this section does not differentiate indoors/outdoors.

RE: 1/2" conduit
See Cahp. 9 Tables - Notes to Tables - #9
"A multiconductor cable ....shall be treated as a single conductor for calculating percentage fill area...."

I've never done the arithmetic but if I remember correctly from a previous post NM would require 3/4" conduit to be in compliance.