Seagate randomly generates keys for their FDE drives, and stores them directly on the drive itself. Presumably, this key is in-the-clear from the point that it's generated to the point that a user sets a password.

Do users simply trust these factory-made keys, or is there a way to regenerate the key?

Also, after the password is chosen, does Seagate use the password to encrypt and decrypt the key that was originally assigned? Or is the assigned key always exposed somewhere, and the password is just used as an access control?

I would imagine that the key is stored on the firmware, not on the disk. So it's not actually in the clear. The password is to protect access to the firmware key decryption routine.