Is it the imperative to be driving near motor insurance?

Answers: Yes. All vehicles must be insured. If you don't, and you hit another vehicle, you will have to rate for the repairs out of your pocket. That can run you in the thousands of dollars. If you also injure the people within the vehicle, you will have to pay for their medical treatments and hospital stays. That too would be contained by the tens of thousands of dollars. It is cheaper to get insurance.
In most (or all) states, you can also hold self-insurance, but that's not practical for individuals; it's only for big corporations beside lots of cash and someone to administer it. You can also post a safety bond, but for that you'd want to have $50,000 lying around reserved for paying for an accident. Insurance is deeply cheaper and more practical. Plus, insurance companies have experience and resources that can come in thoroughly handy sometimes.
Yes. Liability is required minimum coverage.
In some states if that even counts anymore, you do not have to enjoy insurance unless & until you have been contained by an accident totaling more then $700
Yes. State insurance laws require you to have a minimum height of liability coverage to protect yourself from lawsuits when you cause an accident and lay waste to other people's property (cars) and hurt or kill others. Most states set minimums that were conceivable years ago when they were established, but are way too low for today's expensive cars and lawsuit-happy ancestors. If you only buy the state-required minimum, you may find yourself being sued for more money.

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