Im really wondering about this specific stat, so can anyone tell me?
And why is it that spell vamp have two numbers separated by a bar?

Spell Vamp works similiar to Lifesteal for melee, except it gives you health back for using spells.

I'm not 100% sure how it works exactly, so I won't delve into it anymore.

spell-life steal
single target spells get 100% of your spell vamp
aoe spells get 33%

so, let's say that you have 12% spell vamp
you hit for 100 damage
single target spell will heal you for 12HP
aoe spell will heal you for 4HP (per target)

So I was right about my first guess, but it didn't work when I tried it. I dont have full hp and tried using a spell but my hp remain the same. Maybe I'll try it later to check again. And yep if this is the case, this stat is really worthless, even for those mages with a high AP.

spell vamp works on anything rylia's scepter does, if your not sure go into prac and but a scepter then see if it slows

Spell vamp isn't a valuable enough stat that you want to go after items specifically to have it. Play morg, since she has passive spell vamp, and see how little difference it really makes outside of laning.

I was under assuption that any form of magic damage sourced from you was spell vamped. Even thornmails passive. Obviously not sure, and probably wrong!