1) After having a severe cold accompanied by nasal congestion, one complained of a frontal headache and the right side of his face ached

(1) After having a severe cold accompanied by nasal congestion, one complained of a frontal headache and the right side of his face ached. What bony structures probably became infected by the bacteria or viruses causing the cold?

In this situation, the bony structures that become infected were the paranasal sinuses. These are not "bones", but rather paired cavities in certain cranial and facial bones near the nasal cavity. They exist in the frontal, sphenoid, ethmoid, and maxillae bones. These sinuses are lined with mucous membranes that are continuous with the lining of the nasal cavity. Inflammation of these membranes is called sinusitis. If the membranes swell enough to block drainage into the nasal cavity, fluid pressure builds up and a sinus headache results.

http://en.wikipedia.org/wiki/Paranasal_sinus

(2) An elderly woman, stumbled while walking, she then felt a terrible pain in her left hip. The x-rays revealed that the hip was broken. Also, the compact and spongy bone throughout her spine were very thin. What was her probable condition?

She's displaying classic symptoms of osteoporosis. This means "holes in the bones." In other words, the mineral deposition in her bones was being depleted for other physiological and homeostatic purposes. As a result, the bone density decreased and the bone mass goes down too. Calcium and phosphate are being pulled from the bone faster than they're replaced. In other words, bone resorption out places bone formation. This leaves the bones weak and brittle. Two particularly sensitive spots where this problem shows up first is the neck of the femur (hip fractures) and vertebrae (slinking posture).

http://en.wikipedia.org/wiki/Osteoporosis

(3) Bone X rays are sometimes used to determine if a person has reached his or her final height. What are the clinicians checking out?

Growth in bone length arises from the epiphyseal plate. This is a layer of hyaline cartilage in the metaphysis of a growing bone. The activity of the epiphyseal plate is the only mechanism by which the diaphysis of a long bone can increase in length. This takes place up until adulthood. As a child grows, cartilage cells are produced by mitosis on the epiphyseal side of the plate. They are then destroyed, and the cartilage is replaced by bone on the diaphyseal side. Eventually, the epiphyseal cartilage stops dividing and bone replaces the cartilage. When this happens, the epiphyseal line forms. This is a remnant of where the plate used to be. As long as an X-ray can detect the existence of the epiphyseal plate, then growth should continue.