Do I need an engineer to remove a wall?
If it is load bearing, yes, and the council will want the calculations. If you are not sure whether it is, that assessment is itself a small job an engineer can do quickly.
What is a producer statement?
A signed statement from a suitably qualified engineer that a design or a piece of work meets the building code. Councils commonly ask for one on structural work, and it has to come from someone with the right qualification and insurance.
CPEng, and does it matter?
Chartered Professional Engineer is the registered qualification in New Zealand, and for anything a council will rely on it usually does matter. Ask, because it decides whether your paperwork will be accepted.
How long does a report take?
A straightforward residential assessment is often a site visit and a week or two for the written report. Consent-critical work can be longer, so ask about timing at quoting stage if a deadline is driving you.