Good morning Audrey,
According to the HIPPA act, your medical records are private, not public and no one can review them without your specific written permission. You can read more here: http://www.hhs.gov/ocr/privacy/index.html.
However, very few rules apply to insurance company questionnaires. With the new ObamaCare, as everyone is calling it, the questions regarding pre-existing health issues is suppose to be deleted entirely. But even that is loosely translated.
You are able to change providers of insurance without hassle. There are reporting factors to aid. But, there are no hard and fast ways to prevent the companies from grilling you to death.
I would question them as the reasons for asking and tell them it should not make a difference. Depending on your state there are agencies to aid with the transition and changes you need to make for your health insurance. I would contact them and request their assistance.
Wishing you well.