In order to have a comprehensive claim done & processed by the insurance company there's have to be a physical damage such as scratched paint finish,body damage or a broken cladding not related to accidents
Those kind of claims doesn't raise your premiums.
If you hood cladding is broken you can process a claim for that.Some times a police report needs to being filled depending on the extend of the damage.I guess you would not need to filled a report with the police.The ironman hood logo is covered if the hood insert it self is damaged,the door have to shows signs of being forced open or vandalized in order to consider that a comprehensive damage.
It works like a health insurance,where you pay a premium for medical expenses & services related to you as a covered individual.
I believe the driver's door hinges should be inspected at a body shop & they'll be able to find a solution for the door.
About the rear door paint scratch also check with a body shop to find out how much can be the cost to restore the finish.If the cost is somehow high for you the body shop can work in your favor to have a paint job done & paid by the insurance company.
A VX paint job isn't so expensive as a regular car because half of the car is poly cladding covers.
Comprehensive is a coverage that is offered to pay damages ocurred to your car when the causes of that damage was related to vandalims such as broken in window,natural disasters such as flooding,paint and/or body damage such as hitting a light pole,etc.