Help! Anatomy Lab Questions!

4. Since hair color is determined by pigment in the cortex and the hair shaft is dead explain the fallacy of a person's hair turning white overnight.

The hair shaft grows from the hair follicle (the base). The hair closest to the follicle (scalp) is new hair whereas hair farthest away from the follicle is dead. Hair cannot turn gray over night because it is a gradual process starting at the base of the hair (by the root) and going up.

For 3,

The current produced by this device burns out the papilla (root), so new hairs can never again sprout from it. By disrupting the blood supply to the root, the epithelial cells surrounding the follicle don't have the nutrients required to dvide

a little lesson on the skin 

The skin is made up an outermost layer named the epidermis, followed by the dermis and the hypodermis.

Epidermis: composed mostly of keratinocytes, cells that contain keratin, the protein that gives skin its toughness (not to be confused with collagen which gives skin its resiliency).
Dermis: a network of elastic dense connective tissue containing collagen as well as sweat glands, hair follicles, sebaceous ("oil") glands, nerve endings and blood vessels.
Hypodermis: loose connective tissue containing mostly adipose (fat) tissue.

The dermis, a connective tissue made up of collagen and networks of elastic fibers which give skin its resiliency, is the layer in which tattoo ink is deposited. The tattooing process causes damage to the epidermis, epidermal-dermal junction, and the papillary layer (topmost layer) of the dermis.

The integumentary system is the organ system that protects the body from damage, comprising mostly the skin.

The integumentary system has a variety of functions; it may serve to waterproof, cushion, and protect the deeper tissues, excrete wastes, provides vitamin D synthesis, and regulate temperature, and is the attachment site for sensory receptors to detect pain, sensation, pressure, and temperature. If these cells were alive at the surface, you wouldn't have these protective benefits as they would be susceptible to environmental damage (such as radiation given off by the sun) bacteria and other pathogens etc.