It depends if you have knocked it out in the distortion world. it would be there or in turnback cave.
Giratina
There's no such item/pokemon. Do you mean Giratina?
Absol is the Pokemon before Giratina. Absol's number in the pokedex is 209 and Giratina's number is 210. This is the one in the Pokemon platinum POKEDEX.
You can find Giratina in the Distortion World.
Giratina
you get giratina
its Giratina's Origin Forme
No, Giratina can't breed with anything.
You cannot rebattle legendary pokemon. (Correction, Giratina is on Platinum ONLY)
if you mean star pokemon, giratina
Let Giratina hold it and then trade it.
210 from Turtwig to Giratina