No-claim bonus is a reward from your insurance provider for not making any claims on the policy. For every claim-free year, your assured sum increases by a certain percentage for the succeeding policy year, depending on the insurer. Do check out the benefit with your insurer.
Yes, there is no limit on the number of health insurance plans you can have. You can choose the same or different insurers for different policies as you deem fit.
Almost all health insurance companies have their presence online. You can easily compare the policies, check the coverage, payable premium, and other terms and conditions. Once you find a plan that suits your needs, you can avail it. In case of doubt, you can consult a financial advisor.