Difficulty: Easy, roughly 1 hour of work
These are side missions available as you progress through the main story. You can find these in the transport district, and play any available by speaking to the robots there.
To unlock more PQs you must progress in the story or speak to players with a blue question mark above their heads. These players give you a specific PQ and at certain points in the game.
There are no missable PQs so you can do them last after completing the story if you like.
Note: My understanding of this is that you must complete 7 different[b/] PQs...But i can't remember.