Can you have both primary and secondary adrenal insufficiency?

Unlikely. Primary adrenal insufficiency means that the adrenal glands are unable to make cortisol. In secondary adrenal insufficiency, the adrenals are able to make cortisol, but do not receive enough stimulation from the pituitary to make normal levels. While it is theoretically possible for one person to have both conditions, neither condition is common, so it would be rare to have both.
Maybe. Primary adrenal insufficiency refers to a problem with function of the adrenal gland tissue itself. Secondary adrenal insufficiency is a problem with the pituitary gland of the brain making acth, a hormone that stimulates adrenal growth. With long-standing secondary adrenal insufficiency, the adrenal glands can become smaller and not function well enough during times of stress or illness.