Comprehensive, or "other than collision" coverage. Under most states policies, it is under Part D--Coverage for Damage to Your Auto. You can select the level of deductible you want. Check with your lienholder as some have strict requirements regarding the deductible you choose.
Collision
C. Comprehensive
NO, liability covers damage you do to someone else's property. Comprehensive insurance covers damage to your vehicle by someone else. If you have no comprehensive, then you will need to look to their insurance for recovery of damages.
It covers damage to your vehicle resulting from an at fault collision with another vehicle or object.
I think that your insurance covers the items that were yours that were stolen, and the company's covers the car damage.
Comprehensive insurance covers damage to your own vehicle as well as third-party damage, while third-party insurance only covers damage to others.
Comprehensive coverage on your auto policy covers fire, theft, vandalism, broken glass, animal collision, hail damage, windstorms, etc. Collision covers hitting another vehicle or object or turning the vehicle over.
Auto liability insurance covers physical damage to the other vehicle if you are at fault. It also covers injuries for parties in the other vehicle when the accident was your fault. It does not provide any coverage for your vehicle, you, or passengers.
Liability Insurance
Yes, you can get auto insurance that only covers liability and property damage. However, you will need to purchase collision insurance if there is a lien on your vehicle.
No. Unless you killed somebody's pet deer, liability insurance is no value. Liability insurance covers the damage you do to somebody else's property or person. Collision insurance covers damage to your vehicle when you strike an object or animal or when your vehicle is damaged by someone unknown, as in a hit-and-run accident.
If you have comprehensive coverage on your auto policy it will cover storm damage to your vehicle, subject to your deductible of course.