I am currently using a white RCA cable to display a composite (usually a yellow cable) video signal. I was just wondering if this will harm any of my components or if it's perfectly safe to use?

I can't imagine it doing any harm. But the video cable is different than the audio cable and you won't get the best performance by using the wrong one.

The video cable should be 75Ohms, which the "white" is probably not...it wont harm anything though.

What impedance is the "white" one? I've always known what the "yellow" one was, but not the "white" one.

What about the red audio cable, would that be better to use...

The red and the white ones are the same. Only the yellow is (or should be) different.

Unfortunately, there's no standard impedance for audio cables---though most manufacturers’ cables are somewhere above 100 ohms. Unless you have a brand name cable with published specs the only way to determine the impedance is the check it.

100 Ohms is the rating for balanced audio cables of the like used in the professional and broadcast industry. Microphone cables are the most common configuration. The output of most RCA or phono-type connections are given at 10,000 Ohms.

Two of the primary reasons of using 75ohm cables for video are for interference rejection and proper bandwidth to allow better signal clarity and accuracy. Beware: not all "yellow" ones are 75 ohm. You will know because the wire itself will probably say so and be bigger.