Do women shoot liquid when they climax? What is that called?

There are two types of fluid that women produce. The first is during arousal and orgasm, when the vagina produces more vaginal fluid and lubrication. Many times during orgasm, women will experience a rush of this fluid, to varying degrees. Women also have the capability to ejaculate, usually when the g-spot is stimulated; some women can achieve ejaculation with intense clitoral stimulation as well. This thin, watery liquid is not urine, though it does travel through the urethra (just like a male's ejaculate travels through the urethra). Here's an excellent resource with information and techniques.

Is it true if a woman or man lays over the edge of the bed that an orgasm will be more intense? Is this a common practice, and is it healthy?

What you are describing, to some degree, is known as autoerotic asphyxiation. This is the practice of inducing cerebral anoxia through self-suffocation in order to (supposedly) enhance orgasm. In layman's terms, that means cutting off the oxygen supply to the brain, which can intensify sensations and produce a light-headed giddiness or exhilaration in addition to the normal sensations experienced with orgasm. It can also cause a quick, accidental death.

There are no concrete statistics about the commonality of AEA, as it is usually practiced in some amount of secrecy, most often by males, and usually only discovered at death. An estimated 1000 people a year die from autoerotic asphyxiation. Based on this information, I'd have to say it is neither safe, nor healthy. Remember Michael Hutchence, lead singer for INXS? There are dozens of other ways of heightening orgasm...be safe.