A)being close to equator helps but not dramatically, logistics are still more important
B)few satellites are actually launched to an equatorial orbit, most of the time you want an inclined or a polar one. If you want your orbit to have around 40 degree inclination NZ is perfect.
There's no "idle thrust" on Falcon 9 since even the lowest thrust is enough to lift the almost empty booster. You also don't want to completely run out of fuel because your engine will probably explode. This was just a residual fire.