To answer your first question, yes 'Controlled Respiration' is a trait that only aquatic pets can have, and with it, allows the aquatic pet to be out of water for a longer period of time than normal. You know how fish act as soon as you bring them out of water right? Well, let's say then if they had this they may be able to still act normal for a couple minutes or maybe even longer if they had this trait
As for 'Heretic of the Faith' I'm actually not really sure... You see, I am still having trouble figuring out how to assign alignment XD
So what I suggest is that you point Kodai in the direction of this question, and just to help her out once she gets here, here's the definition of the trait, (which she probably already has memorized anyways X3)
Heretic of the Faith - Your pet strays from the teachings of its faith and changes alignment one step (Lawful/Chaotic to Neutral, Neutral to Good/Evil, etc.).