The damage to the gas pump, pump handle and hose would likely be covered under the property damage portion of your liability coverages. This coverage typically covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident.

You will need to check with your insurance provider though to make sure driving off from the pump with the pump handle in still in your gas tank falls into this category for certain and specifically with regards to your car insurance policy.

As for damage to your vehicle, it may be covered if you have physical damage coverages of collision and comprehensive. Likely if the attached pump handle caused damage to your vehicle it would fall under your comprehensive coverage, but again read through your policy and check with your insurance agent.