[b]Could we get more details on how the elements work?  I'm kind of undecided as to which one to go for ^;^[/b]

The elements are very basic manipulation. Shape them, shoot them, channel them through weapons, all that.

In the upgraded forms or M=D, they become more advanced and even versatile, spreading into advanced stuff like blue fire, ice and all.

The idea is to keep the base form abilities simple and the upgraded form abilities 'advanced'.

Fire becomes stronger, hence becoming blue fire.
Water, when enhanced, upgrades into stronger water manipulation and spreads into ice manipulation.
Earth, when enhanced, can control stuff as hard as steel, diamond and even control earthly things like gravity.
Wind, when enhanced, controls other aspects like lightning.

Other abilities exist outside these, even if they're not 'main girls', like poison, heart, and even some less conventional abilities.

[b]I mean do the elements work like in the Avatar series, or are they more esoteric (the representations of the elements such as wind and the connection with mind or fire and its ability to cleanse corruption), or both, or neither??[/b]

It's more like the former. Stuff like mind/heart abilities are seperate abilities altogether and exist outside the main four.

EDIT: Edited the app to include an 'enhanced form abilities' section.