Alchemical Synthesis is a virtual crucible wherein the Elements, represented by color-coded corpuscles, attract or repel based on affinity. Two or three may fuse together, conferring new abilities. If all are moved into the Circle of Consolidation in the center, a process called individuation occurs, unlocking a character's full potential. This is accomplished through personal interactions, which leave an imprint on the psyche. When you think about it, alchemy is all about the Elements, so why shouldn't Elements be all about alchemy? ;)
This too is a metaphor. It's not about literal, physical substance transmutation, but allegorical transfiguration of the spirit, whereby the corrupt energies of hatred and bitterness are purified and undergo metamorphosis to become a love just as strong, facilitated by acceptance (of the self and others) and compassionate understanding by means of empathetic insight.
It's about a heart of lead turning into a heart of gold, not literally transforming lead into gold. The ancient alchemists were on the right track, but their eyes were blinded to this truth by lust, greed, pride, envy, and the rest of the Seven Evils. Now, however, we see the meaning of alchemy in a new light, and it's all thanks to the Virtues: charity, kindness, purity, humility...
All characters and their Elements are gauged along the spectrum of Anima and Animus. This is a measure of the degree with which they attract or repel feminine and/or masculine Elements.
In Cross-Element Fusion, discrete corpuscles combine into Elemental molecules, granting new abilities. A character's Elemental chemistry is influenced by their interpersonal relations, as well as any Elemental spirits they've captured.
From the beginning of the series, all characters have possessed their own native Element. In E7, by integrating Elementals, they may gain secondary Elements (such as Fire/Air), which will boost their compatibility with others, expand their own skillset, and increase their potential for Alchemical Synthesis.