It's usually recommended to add everyone who lives in the household on the same policy if it's likely they will be driving the insured car, and insurance companies generally require everyone in the household of driving age to be listed on the policy. But if the others in the household already have their own insurance and vehicles, this would be unnecessary.
Yes, you can insure a car that you do not own. You will need to list the owner of the car as a driver since they will have access to the vehicle.
Car Insurance Costs
Insurance companies generally require that any person living in the household be listed on your policy regardless of driving status. If a member of your household won't be driving your vehicle then you can normally exclude them from coverage or have them listed as a non-driver.