You need all the other limit breaks (for levels 1, 2 and 3) to be able to use the level 4 limit manual. However, Cait Sith can never learn his level 4 limit break (he only has one limit break on levels 1 and 2).

As for the Counter materias, there's several places in the game where you can get the Counter Attack materia. I think you can only get Magic Counter from Chocobo races. Counter is kind of hard to find. It's in the Northern Crater. Follow Zeromus_X's instructions to reach an area with a very bright light in the center. I don't think you can see the materia, but keep going around the light and tapping the confirm button, and you should eventually be able to find the Counter materia.