What are symptoms of an aortic valve prolapse?

Maybe none. Av prolapse results in aortic regurgitation. Even if it's severe, it may take decades before symtpoms occur, if ever. Symptoms when present may be breathlessness with less than usual activity, anginal type chest pain, or spells of passing out/nearly passing out.
Shortness of breath. If the aortic valve prolapses, it will leak and produce the same sympoms as other types of aortic insufficiency. So the primary symptom would be shortness of breath. The amount of leakage would determine if there are symptoms and how severe they are. Other symptoms might be palpitations, fatigue, or chest pain.