Do women with addison's adrenal insufficiency have low estrogen?

Not significantly. The adrenal glands produce hormones which are precursors to estrogen, but that only comprises a small amount relative to what the ovaries make. Ovaries are the source of most estrogen in females. If menstrual cycles are irregular in properly treated addison's disease, autoimmune disease of the ovaries may need to be considered also.
Not necessarily. However if both are present (i.E ai and premature ovarian failure) then a condition called autoimmune polyglandular syndrome may be the underlying cause. Checking thyroid and calcium levels in addition to fasting glucose is needed to make sure no additional endocrine deficits are present. Obviously this must be done under the care of an endocrinologist. Good luck.

Related Questions

Is there a difference between adrenal insufficiency vs. Addison's?

Can be the same. Addison's disease is primary adrenal insufficiency and implies destruction of the part of the adrenal gland which makes cortisol. Secondary adrenal insufficiency is when the pituitary gland doesn't make enough acth, a hormone which signals the adrenal gland to make cortisol.