Only two core wires, is it secure?
The security light with remote control is double insulated, so it is safe without earth wire. You may need junction box to install it, which is not included in the package.
Movement is triggered within 5m e.g. not exactly 6m, is it faulty?
The sensing distance is set in 3 levels, 6m /9m /12m, while it will be affected by the surrounding selements, and movement goes like fan-shaped (not go straightly towards to light) will trigger the sensor easier and more sensitive.
The light is constantly on, how to set it to detection mode?
Press the ON/OFF button, the light is constantly on. If you press again to turn it off, then press DAY or NIGHT mode, the light goes to detection mode.
Is it solar powered?
No, it is corded power, voltage is 230V AC and frequency is 50 Hz.