Water -> Ice (molecules are slowed down prevents friction and heat therefore it cools down.)
Earth -> Gravity (the mana in the air forms into the "rigid" earth quality and the mana turns heavy. making gravity)
Earth -> Metal (maybe dwarfs have insane control over earth and can control the small impurities in metal)
Earth + Fire -> Magma (magma is molten earth, basically just a different form of earth)
Water + Earth -> Plant (like how humans have healers(which i assume is accelerating the mana in the meridans which fuel the body's energy), elves basically use the same understanding and speed up the growth process of plants at high speeds.)
Air -> Sound (vibrating the air molecules into a tuned sound)
Healing Magic -> (accelerating the mana in the meridans(mentioned when Arthur had a mock battle against that one guy in Tess's squad.) which circulate mana through the body healing small wounds and getting rid of impurites. what healing does is: accelerating that process. speed up the mana flow.)
but how does fire turn into lighting? maybe...theory btw:(the radio waves, gamma rays, and X-rays, are forcefully separated for a fraction of a second and they slam back together creating a lot of friction which ignites the air, creating lightning)