Recommendation:
Aeroth (Air), Solmat (Solid), and Iqora (Liquid) should not have races. All life uses these.
Speaking of life, Gaea (Life) should also not have a specific race, as it is all races. It can, however, be an element (just not the entirety) of some schools.
Rather, if you want to go with elemental races, break down Maanag (Energy) into:
Velectro (Electricity/Lightning)
Achemada (Chemical Reactions and Transmutations)
Korimac (The fueling of the Terra Core to facilitate major geological changes such as earthquakes)
Necronimac (Necromancy, this is not entirely life as it really just involves [i]animation[/i], although used on once living minds)
Hydizeph (The commanding of winds, used to create tsunamis are blow away villages)
My racial recommendations are, respectively:
Nodogi (Tinker Gnomes)
Negoski (Trolls but Russian-influenced instead of Jamaican)
Stodig (Classic dwarves, but mage and stone working-based instead of ironwork-based)
Azarliche (A population-dominant lower class of ghouls and zombies infinitely loyal and obedient to the scentient nobility of lich-spectres, this would be a fallen elven kingdom based on Shakespearian London, subtracting some tech levels and adding classic medieval fantasy elements)
Ilvia (Essentially whimsical high-elves, although not particularly prude. They are more like half-elves, except territorially and with cultural openness they replace humans.)
The names come from latin and greek variants, as well as some mythical linguistics and DnD vocab. As it is your RP, feel free to tweak or change as you please. This is just an idea to essentially combine the sects of what everyone usually wants to play. For every major race I have come across, they can fit into here or at least be a sub-culture of one of them.