Hypercalcemia causes both systolic and diastolic hypertension, AFAIK.
Diastolic blood pressure is mainly dependent on peripheral vascular resistance (not atria). Contraction of vascular muscle cells depends on intracellular calcium levels, which is affected by serum calcium levels. Simply: More calcium in serum > More calcium in the cell > Contraction > Increased PVR > HTN. This is also why calcium channel blockers (like amlodipine) produce vasodilation.
For osteoporosis, hypercalcemia itself doesn't directly cause osteoporosis. Rather, it's the underlying pathology that results in osteoporosis. For example, think of the effects of PTH on bone in primary hyperparathyroidism. What would be the chronic result of bone resorption stimulated by PTH?