Can secondary hyperparathyroidism be caused by a vitamin d deficiency?

Yes. This would generally be in the case of severe or very low vitamin d over a period of time. In such a case, the calcium would drop and increase the work of the parathyroid gland.
Yes it does. Yes Secondary Hyperparathyrodism can be caused by VitD Deficiency.
Yes. Secondary hyperparathyroidism can also be caused by low calcium and/or low magnesium intake, even with adequate intake, poor digestion (poor pancreas function, certain liver problems, etc.) or poor nutrient absorption (celiac disease, intestinal removal or bypass, etc.) can lead to deficiency.