What is the reason for sweating on the commode and on the flush tank in the basement toilet which causes leaking to the floor?

The only reason for "tank sweating" is temperature/moisture differential. The water in the tank is colder causing "contact condensation" in the air surrounding the tank. The primary reason is high moisture content in the "ambient" air. Plainly put....You should purchase a decent dehumidifier to rid the basement of the damaging moisture. Thank your luck stars that the tank is your "barometer" and not the mold factor!!!!!!!! MOLD is next!!!!!!!!! Y-THINK-Y This happens when the water in the tank is much cooler than the room temperature. Some people get water heaters to heat the water going to the toilet, others get tank covers. You can get them at places like JCPenney or other bath supply stores. Simply wash the tank cover regularily so it doesn't cause a mildew problem.