monster Monsters. Help,advice section

Here's a few quetions to start it off.
1:Is twilight odin actually good? He takes forever to lvl up, he's weaker by far then my red chocobo, his hp and defense sucks, but everyone says he is the strongest monster you can get without dlc. Can someone tell me if he sucks, and if not, tell me how to raise him up right to fix him.
2:Where can i find the different chocobos? I know where the red, ravenger, green, silver, and normal chocobos are, but i can't find the rest.
3:Any tips on raising the chance to get a monster crystal? Evertime i see a monster i like, I rage on it and finish it off with my current monsters move, but it it doesn't seem to raise the chances like the game says.

please help

thanks

Actually, i don't think i do have the monster fragment skill. I also forgot to mention that I know were the purple one is (the snowy time, with the red chocobo's you can ride, of the area you met the girl who works with hope later on. From the academy, go up the stairs I think once, then look right. IT's usually right next to the pile of rubble you can't jump over. Sorry, Can't remember her name, the name of the area, or it's time) But thanks for the white one. Do you have any idea about the gold chocobo or the black ones. I've heard the gold one is at the end of time where noel came from, but i can't find it anywere.