Can water freeze below 0 degree celcius?

Yes it does hence the term freezing point

From the Wikipedia entry on supercooling: "Water normally freezes at 273.15 K (0 °C or 32 °F) but it can also be "supercooled" at standard pressure down to its crystal homogeneous nucleation at almost 231 K (−42 °C).[1] If cooled at a rate on the order of 106 K/s, the crystal nucleation can be avoided and water becomes a glass. Its glass transition temperature is much colder and harder to determine, but studies estimate it at about 165 K (−108 °C).[2] Glassy water can be heated up to approximately 150 K (−123 °C).[1] In the range of temperatures between 231 K (−42 °C) and 150 K (−123 °C) experiments find only crystal ice.

Droplets of supercooled water often exist in stratiform and cumulus clouds. They form into ice when they are struck by the wings of passing airplanes and abruptly crystallize. (This causes problems with lift, so aircraft that are expected to fly in such conditions are equipped with a de-icing system.) Freezing rain is also caused by supercooled droplets."

I believe water freezes at or below 0 celcius under standard atmospheric pressure.

Sure. Just add salt. Or change the ambient pressure.

Colloid; (Electrokinetic phenomena)water freeze at 0 degree celcius,pure water at -40

Yes... that's when it does freeze 0 and/or below (Celcius) / 32 Farenheit

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