Stats?

Ode of Sighs says something about affecting stats, but Mabination and Mabidata aren't being clear cut about it. Just which ones are affected?

Hymn of Life increases recovery rates of HP/MP/Stamina. Odes of Sigh decreases Movement Speed, Attack Speed, and Casting Speed of enemies as well as their Str, Int, Dex, Will, and Luck. Straight from the JP wiki. Does not apply in Guild Battles or arena, at least not in JP.

Casting speed as in magic? What about loading speed of all other skills?

Pretty much the speed of the enemy in general, so yes, normal skills too.

Another thing, it's just one circle, not two different colored circles for Phantasmal (I refuse to call it Fantastic)? How to tell the difference for Hymn and Odes?

Different skills activate different types of circles, so if you use Battlefield, you know it's Hymn and not Ode.