Mangawhai runs on a different calendar to mainland Auckland, and the single most useful thing to understand about the place is that published hours are a summer statement. A kitchen doing dinner six nights in January may do two in June. A cafe may shut at lunchtime midweek. None of this is on a sign anywhere, and knowing it saves you driving twenty minutes for a closed door.
The general shape
Broadly: cafes run seven days through summer and drop midweek days in winter, with Monday and Tuesday the usual casualties. Restaurants contract from most nights to a Wednesday-to-Saturday or Thursday-to-Sunday window. Beaches and walks are unaffected, just colder and emptier — which is an argument for the off-season rather than against it. Ring the specific place; do not reason from this paragraph.
The off-season honesty
May–August, more places are closed than open on a given Tuesday. That's a feature for locals (we get our village back) and a frustration for visitors. Plan around it: arrive Thursday or Friday for the better selection of open kitchens.