I flew WLG-CBR-SIN earlier in the year, in J, Award booking, but not via Krisflyer.
The tax and charge breakdown was
F1 USD $2.40 (New Zealand Border Clearance Levy International Departure)
Kk USD $11.29 (New Zealand Passenger Service Charge International Departures)
Ia USD $8.60 (New Zealand Passenger Security Charge International)
This was not booked via SQ, so perhaps SQ are charging it incorrectly.
As to transit visa - you should really check this on the embassy website. It's unlikely to be needed as you do not pass immigration, but I do not know your nationality.