If my mother was diagnosed with MS and is still living with the disease, will I get a lower rate because of her relation to me? MS isn't a genetic disease that can be passed down so I think it would be unfair for me to have to pay more for a disorder my mom has.

No, you shouldn't be penalized for this. My understanding is life insurance companies are mostly concerned with family history of heart related conditions and cancer. If someone knows otherwise, please correct me.

Solutions is right. Stay away from poorly rated companies. Size doesn't matter in this case though. Look for an A rated company like American General Life or other. A rated companies will be around to payout.

Each life insurance company has their own set of underwriting guidelines and classes of risk they will accept based on several factors including family history.
 
Usually life insurance companies are concerned with health history of your parents / grandparents, and any history of cancer, heart disease, or other health conditions requiring medication, or those which may reduce your life expectancy.
 
In addition, your personal health history and current health is important, as well as any medication you may be taking, or have taken in the past for a health problem.
 
There are many insurers which specialize in insuring people with high risk medical conditions. Also, there are insurers which offer life insurance no medical exams policies, and no medical question life insurance for people who have been declined, are having problems getting life insurance, or just don't want to take a physical exam.