@1)... um.. they morph hair all of the time... did you mean like if they were wearing a fur coat or something? And I'm pretty sure that hair does contain DNA, and either way, the plans for producing it are included in DNA. Or are you referring to hair length? Well, there isn't a canonical answer for this in-series, but we theorize that the morphing tech must record some physical features as well, such as hair length, height (which also isn't based on DNA), fat/muscle proportions, etc.
@2) Book #29, The Sickness. He was sick with some disease, and Aftran infested him to find out how to help him, since Ax was de-de-delirious!