What's the approximate outer diameter of the pipe?
All along this pipe there are water droplets. I, being a new fix-it person, do not know if it is a supply pipe from outside or not. I think that the chances are good that it is. Our temperature in the basement is cool and the outside air temp is a bit lower but not drastically.
All you need is very cold incoming water and high humidity and you'll get condensation
Check all the toilets to make sure they dont leak through..........