Is there a large genetic component to cerebrovascular disease?

Not really. Though there are rare genetic stroke syndromes (eg cadasil), for the vast majority of strokes, risk factors with a strong genetic component (hypertension , diabetes, high cholesterol) are the much bigger contributors to strokes and heart attacks often running in families (getting these diseases increases risk of stroke).
Yes. Cerebrovascular disease causes strokes. A tendency for strokes can run in families. Especially related to blood pressure problems, diabetes, cholesterol problems, smoking habits, drug use, etc. Vascular malformations including avms and aneurysms can also show a genetic tendency. Markers are available to uncover possible risks. Discuss with your doctor.