What is this black and white worm in a white case?
This is just a larva of a moth from the Family Tineidae, most probably Phereoeca uterella (known as plaster bagworm or household casebearer), or Tinea pellionella (known as case-bearing clothes moth).

As you can see, the larva of this moth...


  ... constructs a protective case from silk and camouflages it with other materials such as soil, sand and insect droppings. (from Wikipedia) 


Here is a better picture of Phereoeca uterella, from the entomology deptartment of the University of Florida:



Here is the imago (adult), for comparison: