The trick to reducing insurance on a beater car is to not insure the car for damage. Just get insurance for passengers, yourself, damage you do to other people, cars and property.

Never insure for a risk you can cover yourself. If you have a car that is worth < $10k, you probably should pay for damage to it out of pocket.

Depends on your car, they said it's a beater. Of course an insurance company will give you significant price reduction if you have, say, a late 90s Toyota Corolla or Honda Civic with a 80 hp engine, as compared to something more modern and fun with twice the power.

GP might be paying only third-party insurance. I'm not sure about America, but at least in Australia, AU$500 (US$400) per year will get you third-party insurance if you're under 25, and if you're driving a beater car you don't need any other insurance.

I looked at getting comprehensive insurance on my old car, but in the end the excess was greater than the value of the car. I wouldn't be surprised if it was the same for GP.

You need liability insurance. I don't think $700 would cover it.