The PA item you're talking about is the PA Fragments. There's a quest where you can trade them in for various PA disks. More info here:
http://psp2.psupedia.info/The_Secret_Society
To select the quest, after clearing chapter 3, select the 4th quest option, and it should be the second one in the list.
The third option on the Job Class Lady is for the Type Abilities you can equip for your class. List of all the abilities(in Japanese and English for comparison) can be found here:
http://psp2.psupedia.info/Type_abilities
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