What explains the low birth weight (<2500 gm at term)?
The maternal history of smoking is the most likely factor. Poor nutrition plays a role as well, which is common in persons abusing drugs.
What vitamin is typically given to newborns to prevent the problem seen here soon after birth?
Vitamin K deficiency explains the findings. The blood coagulation factors (II, VII, IX, and X) made in the liver require vitamin K as a cofactor in carboxylation of glutamate. A deficiency leads to a coagulopathy with abnormal bleeding, so called "hemorrhagic disease of the newborn". The most serious consequence of this could be intracranial hemorrhage. Once the bacterial flora of the GI tract are established, there is endogenous production of vitamin K to produce most of the daily requirement.
What is a contributing factor for the cellulitis?
Vitamin C deficiency is present. Vitamin C is needed to hydroxylate procollagen in order for form stable connective tissues. A deficiency of vitamin C is called scurvy. Wound healing requires adequate connective tissue formation with collagen.
How do you explain the anemia?
Iron deficiency along with the Vitamin C deficiency are present. A deficiency of vitamin C results in poorly constituted capillaries and venules from which bleeding can occur. The bone matrix has deficient type 1 collagen with scurvy, leading to skeletal deformities in children as well. The world's most common nutritional deficiency is iron. Iron is needed to form the heme in hemoglobin. Children need iron as they grow and need red blood cells.