What is this white powder on the walls and around the plumbing?
Efflorescence!  Efflorescence is a crystaline deposit of water-soluble salts on surfaces of masonry, stucco or concrete.  Water brings these salts to/toward the surface and then the water evaporates leaving behind the crystaline deposit.

Note: If one has efflorescence on the surface, one can count on having similar deposits just below the surface, too.  These sub-surface deposits tend to cause crumbling of the masonry, stucco, or concrete structure.

The presence of mineral deposits on water pipes indicates one of three things:

1) there's a pin-hole in the pipe through which water is penetrating and evaporating to leave behind calcium (and other minerals) behind,

2) water is leaking from a fitting and leaving behind deposits, at the lowest point of moisture travel, before dripping or evaporating,

3) water is carrying minerals from an adjacent wall, ceiling, etc.; which runs down the pipe and leaves behind deposits, from the lowest point of moisture travel, before dripping or evaporating