Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.
No. Third-Party Car Insurance is obligatory for all motor vehicles. Third party risk insurance is compulsory under the statute of the Indian Motor Vehicles Act, 1988. You may be a good driver, but it does not negate the fact, that the vehicle you drive can become the victim of a disaster that was caused by another vehicle. In such a situation, you will be grateful that the driver involved has a third-party car insurance cover that you can raise a claim on.
Making a third-party car accident claim can be as simple as writing a letter. If you believe you have a valid third-party car accident claim, contact the responsible insurance company via telephone as soon as possible to inform them of the claim (you should have taken down the other driver's insurance policy information at the car accident scene). This is called “giving notice” and is often overlooked. Proper, prompt notice can mean the difference between recovery and walking away empty-handed.
The Insurance Information Institute suggests that you take the amount you'd pay in one year for comprehensive and collision coverage, and multiply that number by 10. Is your car worth less than that number? Then comprehensive and collision coverage might not be a cost-effective option for you. In other words, you might want to talk to your agent about whether it makes sense to include these coverages on your car insurance policy.