A third-party liability cover provides monetary compensation if damage is caused to a third party's car or property due to accidents. This, however, does not cover any damages caused by illegal driving in any manner.
The most important document is the registration certificate. Apart from that, make sure to ask for the original invoice of the car, road tax receipts and a no-objection certificate from the car financier.
Term and health insurance both serve different purpose and are equally important. To secure yourself, availing both term and health insurance policies is never harmful.