Why do different people have different premiums?
The premium is calculated on the extent and nature of the cover you want. A higher sum insured means a higher rate of premium. Similarly a higher risk will be charged a higher premium. An example of this is that an older person will have to pay a higher premium for health insurance for the same sum insured. Sometimes the risk is higher depending on the location of risks - for example in motor insurance in areas where accidents are higher. So the premium will vary according to the nature and severity of the risk.
If I buy a policy and don't make a claim, it is a loss. So, why should I buy insurance?
General insurance is not meant to be for savings or investment returns. It is meant for protection. What you pay for is the protection against a risk. To approach it as something from which returns should be obtained is not the correct approach as there is a price to pay for protecting a property worth lakhs for a few hundred rupees.