Name all the living cells of bark and include a reference.

The term bark refers to the covering of cells on the outside of stems and roots and includes both the inner and outer bark.

The part that is the outer bark consists of dead old cells that are for protection for the living cells of the inner bark. This inner bark is called secondary phloem tissue. Phloem cells are vascular or conducting tissue. Their purpose is to transport food from the leaves down to the roots. There are also tough cells which act as a defense against organisms that try to eat through the tree's bark or that wish to attack the tree. It lives for awhile before becoming cork. 

A meristem tissue called cork cambium produces cells of the outer bark which get pushed to the outside along with inner bark which are pushed inward. These cells remain alive for a time and respond to growth hormones called auxins. They are part of the phelloderm which contain cells that have cell walls that allow exchange of respiratory gases and nutrients. The outer cells of the bark become unable to exchange gases due to their waxy nature and soon die. However, they provide a water-tight outer covering for the tree.

The outer cells of the bark protect the underlying living tissue of stems and roots. I have included a labeled diagram with an explanation of bark and the anatomy of a tree.