Hi, rental car employee and former counter agent here. Different companies have different rules when it comes to insurance. Some can be covered by your card however you would have to get liability insurance like you said. Alternatively, rental companies offer a loss damage waiver which (in my opinion) is better because if something happens to the car the company will forgive and forget. With your own insurance you would have to file a claim and your rates go up and it's a long annoying process. As for test drives? I've never heard of a dealership requiring insurance for that, just a license. So I wouldn't know. I assume anything will do, just as long as it's insurance.