Mordecai can indeed be either gender, but only Knights of the White Lily are women. Adharism is a more intense form of an anti-magic field with a much shorter range (like you have to be right next to them more or less, or at the very least a few feet).
To cover the subject of Mordecai first, I think the proximity of their anti-magic field is generally dependent entirely on the player themselves, just as a person making a Serenian can decide if their character is extremely allergic to iron, or only has a slight aversion to it, etc. It's possible that an Adhara's proximity field might have an affect on magical areas, since inanimate magical items are affected by their powers as well. I believe that's another case where the specified potency the Adharism is up to the player. If they're field is strong enough to disable magical areas of effect, that might be entirely plausible. But I think it's also fairly possible that an Adhara's gift probably applies only to people and things, rather than places and parcels of enchanted land. If there are more questions regarding this, you could probably PM Rhi for specifics.
I think the separation between mortal magics and immortal ones separate them between a divine level and a very 'physical' one. Immortal magics include divine powers (Gods, spirits, demons, etc.) and the powers given down by those. Mortal magics include nearly everything else, elemental magic, primal magic, etc. I believe race abilities, if it's indeed magic would likely be affected by a Mordecai's anti-magic field (but remember these facets are entirely up to the player, to keep things more or less evened out) and would thus be included in mortal magics, whether the character is apart of some fantastical race or otherwise. It would make sense if you think of 'immortal' forces as beyond the mortal plane of existence.
But most of these things are generally free to the decision of the player.
I think you have the gist of it more or less, and if there was any confusion, I hope I was able to clear something up for you. (: