Mandatory car insurance is generally just liability insurance so that, if you are at fault, your insurance will cover the repair to the other car. Most car loans require you to also get collision coverage until you have paid off the loan, but that is not a law, more of a contractual agreement. I am not sure what you mean by universal insurance. If you mean a plan from the government, I don't see why the government needs to cut into a private market. If you mean free car insurance, subsidized ...
Should I buy car insurance when renting a car?
Now if you lend your car to someone and decide to a rent a car as well, your rental car would not be covered, because now the insurance company is covering two cars when it did not agree to. So no, as long as you have your own insurance you should never really even think about buying the insurance from the rental company.
What should I avoid when buying car insurance?
Stay away from nationwide and progressive. They both jack up your rates with no cause and drop you when you have a accident. Got dropped by both because of a accidents, not at fault, and the other drivers gave false info. Stay away from companies who deal with multiple insurance companies.
What should I not do when renting a car?
Do not listen to the other person that responded to you (although they were right about the rental car stuff). Insurance ALWAYS follows the car. You insure a car, not a driver. If you let someone drive your car and they get into an accident, then the proximate cause of the accident was you for letting them drive your vehicle.