1. Reflexology is a branch of 'alternative' medicine based on the concept that there are zones on the feet and hands that reflect certain areas of the body; and manipulating these zones (or reflex areas) promotes healing through one's 'Qi', which is a pre-science notion meaning 'vital life force' - a concept invented by ancients who had no idea of how living organisms work. No plausibility or evidence exists for Qi.
Example of its use? People use it primarily for pain relief, but reflexologist claim to be able to treat all sorts of conditions, such as: arthritis, osteoarthritis and osteoporosis, water retention, reduction of inflammation, hormone balance, fertility, etc etc..
2. Most people do not use reflexology.
3. The biggest population uses would be by people who are gullible, have little understanding of science, nature and reality, or vulnerable people who are willing to try anything no matter how crazy when nothing else seems to work. As to where these populations exist can't be determined as alternative medicine typically does not keep such data and reflexology has no proper regulation. Though I'd suggest new-agey areas may attract many reflexologists.
4. The main risk associated with reflexology would be if it is used in place of proper medical treatment for serious conditions.
5. Advantages: its relaxing, it's relaxing and it's relaxing. Disadvantages: standard foot massages are cheaper, it promotes uncritical thinking, and the placebo effect does not work for everyone.
I guess they haven't discussed clinical trials or scientific plausibility with you yet huh? I hope you aren't paying too much money for this.