When you are applying for a health insurance policy always mention pre-existing disease in the proposal form and in detail.
Also read - When Pre-existing disease will be covered?
If a person in your family has some disease then it's better to go for a separate policy for that person not family floater. (How much health insurance do you need?)
Every company pay claim (see no reason why they will not), if you are claiming with in the Terms and Conditions of the policy. So read T&C of the policy document carefully (specially co-pay etc).
Also read - How to prevent rejection of Health Insurance Claim?
Health care is very costly now a days and if you are living in Metro opt for Sum Insured Accordingly.
Also read - Tips to SAVE Health Insurance Premium