1. The patient is likely suffering from Addison's disease, characterized by decreased adrenal cortex hormones including cortisol. Cortisol deficiency results in hypoglycemia and hypocalcemia.
2. Cortisol increases gluconeogenesis in the liver and decreases glucose transport and utilization elsewhere, resulting in hyperglycemia. It also increases calcium excretion and inhibits bone growth, worsening hypocalcemia.
3. The pigmentation of the gums is caused by increased levels of ACTH and TSH due to loss of cortisol negative feedback, releasing more melanin from melanocytes.