About a month ago, when touching a cold cheese, my hands felt simultaneously freezing and on fire. Now this happens when I touch anything that's even slightly cool. What can it be?

You are describing 'paraesthesiae' - abnormal feelings in the hands that may denote problems with your circulation to them or to the sensory nervous system from them. These feelings have several causes, from trapped nerves in the wrist (carpal tunnel syndrome), elbow or neck, to Raynaud's syndrome, in which the blood vessels in the hands narrow and the resulting poor circulation leads to disturbance of sensation. They may even be a sign of a vitamin deficiency (perhaps of vitamin B12 or folic acid) or of a more severe central nervous system complaint. This last is probably the least likely, but should be ruled out, so please see your doctor.

Is there any health benefit to hard water, given its higher mineral content?

Years ago it was postulated that hard water did give advantages over soft water in prevention of bone disorders, heart disease, tooth decay and possibly kidney complications, but I know of no large controlled trials or surveys that convincingly show that people in hard-water areas have less illness or survive longer. I'm very willing to be disproved, however. We live in a hard-water area, and have a high heart disease incidence; we used to live in a soft-water area with low levels of heart disease. The reason for that difference almost certainly lies in social and economic circumstances, and in eating habits, rather than in the water.

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