Mind buttressing armor grants the wearer a +2 resistance bonus on Will saves and renders her immune to possession and mental control (including charm and compulsion effects like command and charm person). If it’s donned by a creature already under the influence of such an effect, the creature immediately receives another saving throw (if one was allowed to begin with) against the spell or effect. If the check is successful, the effects are suppressed until the creature removes the armor, after which they resume. This ability can be applied only to medium or heavy armor.
Emphasis mine. If you take a regular breastplate and enchant it with mind-buttressing, what happens to it when the breastplate becomes mithral?
I know mithral breastplate still requires medium armor proficiency, so does it count as medium armor or light armor for the purposes of special abilities?
If not, then does the timing in which the ability was "applied" matter? That is to say, if the Mind Buttressing ability was applied to the breastplate while it was a legal target, could it still be used if breastplate is no longer a legal target?
Could I also apply the Brawling enchantment to a Mithral Breastplate?
The wearer of brawling armor gains a +2 bonus on unarmed attack and damage rolls, including combat maneuver checks made to grapple. Her unarmed strikes count as magic weapons for the purpose of bypassing damage reduction. These bonuses do not apply to natural weapons. This special ability does not prevent the wearer’s unarmed strikes from provoking attacks of opportunity or make the wearer’s unarmed strikes count as armed attacks. The brawling ability can be applied only to light armor.
Emphasis mine. The same questions apply but in reverse.
Is it ever possible to have a Mind-Buttressing & Brawling Armor?
Being mithral doesn't change the category armor falls into, it just makes it count as one lighter for certain limited purposes, which AFAIK do not include what special abilities can be applied to it. So a breastplate is still medium, so mind-buttressing works and brawling doesn't.
Is it ever possible to have a Mind-Buttressing & Brawling Armor?
Nope.
Emphasis mine. If you take a regular breastplate and enchant it with mind-buttressing, what happens to it when the breastplate becomes mithral?
How is it "becoming" Mithral?
Unless you're using some sort of spell or special ability, once an item has been crafted from a particular material then that is the material it is made out of.
I know mithral breastplate still requires medium armor proficiency, so does it count as medium armor or light armor for the purposes of special abilities?
I would assume that it does still count as medium armor for purposes of enchantments. Unless the weight of the armor is relevant to the feature. In the case of Mind-Buttressing I'm not sure why it can't be applied to light armors. It seems like a weirdly specific requirement that is not explained.
Could I also apply the Brawling enchantment to a Mithral Breastplate?
IMO you would not be able to put brawling on it for the same reason you can put Mind-Buttressing on it.
Only one of the 2 enchantments are going to be legal to apply to the armor regardless of how you interpret how the mithral interacts with the enchantments. This is because the enchantments get added after the item has been created. So I don't see a way to create the item, enchant it and then somehow make it a different material type to allow it to qualify for the other enchantment.