I'll try to answer as best I can:
1. ZES: although this is a gastrin secreting islet-cell tumor of the pancreas, it is associated with something called MEN I (Multiple Endocrine Neoplasia I) about 25% of the time. MEN I usually involves increased secretion of parathyroid hormone by the parathyroid glands, which would result in hypercalcemia.
2. Chronic Vitamin A toxicity: According to Robbin's Pathology, Vitamin A enhances the division of osteoclasts. Thus, more osteoclasts = more bone resorption = more calcium in the blood AKA hypercalcemia.
3. Hyperthyroidism: I would think its due to the increase in bone resorption as a result of thyroid hormone.
4. Addison's Disease: your guess is as good as mine on why hypercalcemia happens here.