A. No
A. No
B. Yes
C. Only if you're on a restricted licence
You must carry your driving licence at all times with your when you are driving.
According to government documents the current fine is $55, although you are more likely to be asked to visit a police station within 72 hours to prove that you are a licenced driver.
Fines are set out in the document Land Transport (Offences and Penalties) Regulations 1999.
As your licence is a valid form of photo identification it's not advisable to leave it unattended in your vehicle. If someone breaks in and steals it then not only will you have to pay for a replacement licence, but there's a risk that someone might fraudulently use the licence, or use information on the licence to identify you in other ways.
Carry your licence on you rather than leaving it.