Who handles the IPO? What happens to shares that are not sold?

Who handles the IPO? What happens to shares that are not sold? (Psst, it has to do with the structure put in place, Best efforts, etc)

Would you rather buy securities on the primary or secondary market? Why?

Give an example of a mispriced IPO, where the price skyrocketed or plummeted immediately. 

Who can participate in an IPO? Do you think this is fair?