Purchasing car insurance is not always necessary when renting a vehicle. Some major credit card companies offer cardholders perks such as car rental insurance just for being a member. To be eligible for car rental insurance through a credit card company, that exact card will have to be used to secure the rental.
Yes it is possible and is done every day. If it is a decent car, you should buy comprehensive coverage for it though to protect it against fire, theft, wind, glass breakage while it sits.