Is it common for faucet handles to turn in opposite directions?
This is contra turn taps usually used for lever handle taps so they both turn away from the wall on a basin or turn both down in a shower or similar if used in vertical eg. Shower above and below you would get normal taps not contras so that they both turn in the same direction which are the ones that you are used to. Also re reading your post it seems that if you have lever handle taps the hot and cold taps shoul be swapped to make them both turn on when turn towards the centre of the basin.