The security code on your phone, your voicemail password, and your billing PIN MAY all be the same number, but they may be different also. They have nothing to do with each other, and are completely separate. You'll need your billing passcode (PIN) to verify that you are the account owner or authorized to make transactions on the account in order to port the number. If you are the account owner, Verizon can ask you some other questions to verify your identity, and then give you the passcode or let you set one if you don't remember it.
Voicemail password is something you set up when you in itially set up your voicemail account. The security code on the phone is the last 4 of the phone number, by default, but can be set to any 4-digit code you want.
Maybe...but not likely. They'll want to verify, confirm, and otherwise KNOW who you are. So a call to CS is your best bet. If you are porting your #, then the receiving company may just need a copy of your current bill/account # or some other proof that it is your account and you are authorized to make the transaction.