Section 334.16(b)requires that NM used in exposed areas be protected with conduit or other approved means. Does the code indicate minimum diameters for various NM sizes similar to the conduit fill tables? Or is the amount of space taken up by the NM irrelevant with respect to conduit diameter? If so is it left to the installer's judgement?

That should be 334.15(b), not 16..typo

You use the circular size defined by the widest dimension of the cable. For flat Romex that makes a pretty fat "conductor". A 12-2 is about .4" which puts it between a #2 and a #1 THHN. Generally I will make some concession if this is a single straight run down a wall.

Yup, it's all spelled out in the code.