I understand that PTK is ultimately the key that is used to encrypt traffic between a device and the WAP after the 4WHS and that the PMK is directly related to the 'passphrase' of the wireless network. What about the PSK? How is it generated and what is its role? And why does the authenticator still need to generate the GTK in the 3rd frame since the PTK is already known in the previous frame?
The PSK is the PMK, it's used to derive the PTK, and it's generated by a function called Password Based Key Derivation Function 2 (PBKDF2).
(The problem with the names PSK-PMK is that some people call the Pre-shared key the "Passphrase" like what you share to people for them to connect, when a Key is actually the 128 bits hex string)
And the GTK it's used for broadcasts encryption, since the PTK it's only for the AP and the station and no other station can listen to that, that's why you need another key.
I think I already answered some of this in here