Her ability to shape-shift is never explained seriously in any form of the canon (she claims it was a wishing well in the movie and comic says a witch, so there's nothing to indicate if she was just literally born a shape-shifter, or it's magic). The way she talks about it and how tied to her sense of self/emotions does make me believe it's more innate than magical, but it could just be she's had magic ability for nearly her whole 1,000+ years of life. Until/if we actually know for sure, I'm okay to lean on the side of caution and make it magical. There's some pink sparkles whenever she transforms, that could indicate magic, and some of her forms only show up when she's emotionally and psychologically in a certain state. Plus, she'd rock a tattoo happily, since they're easy to get at the start.

Thus, her underwater breathing is basically however long whatever sea animal she turns into can go without surfacing.