I really want to understand how this is supposed to be calculated so I do it properly when analyzing properties.

Also, assuming you are properly pricing it, anyone trying to do a private sale without an agent is most likely going to try to get you at a discount knowing you don't have it listed with an agent.It's free to interview agents, so you should speak with 2 or 3 and make sure you're maximizing your return.

NZ is great place to live and bring up family BUT most towns are slow to growth and the rent to price ratio is pretty low, hard to get  proper cash-flow and cash on cash return unless you put big deposit. 

I know every broker is different, but how did yours react?

I plan to do everything legally (if this is legal) with rental contracts and proper paper trail.If YES, would it make sense to rent at my mortgage rate or standard rate?

It doesn't make any sense to charge a well prepared investor 6% when they know how to stage the property properly, and price it right from the beginning.Would love to help you but unfortunately i am not in your area:(

Pmi may cost .500% and if planning properly, may only last 3 to 5 years if you are prepaying your mortgage and the property appreciates.

In the event of a catastrophe, I want the piece of mind to know that the conversion was done properly and the bedroom are legal bedrooms.

Gilberto Grajeda you sound like you have the proper motivation to make you successful!

put the tenant on a month to month and train them properly.