How would my insurance claim work?

My parked car underneath my metal carport collapsed onto my car due to a natural disaster(snow). I have car insurance and homeowners insurance with the same company. I'm a first time home buyer so this will be my very first claim.

Would homeowners cover it all?
What if I don't want a new carport?

The car was a 2005 Honda Civic Sedan LX with 150k miles in good condition.

You report this to the insurance company. The insurance company sorts out their policy on how this is handled.

Homeowners should cover it all. The cost of the vehicle will be covered based on book value for that vehicle. (So, not much since it is so old.)

As for replacing the carport, that depends on how your insurance policy is worded. In some cases, you only get compensation for REPLACING the destroyed or damaged part of the home or covered out buildings. Basically, insurance will cover the cost of removing the damaged structure but if you don't intend to put up another structure, you might not get replacement cost reimbursed for that damaged carport.

Be mindful that you are responsible for maintaining the snow so it doesn't cause damage. If the snow just kept coming and you haven't had a break to clear it off the roof, than you aren't responsible. If you haven't been keeping it off the roof than it's likely that insurance won't pay.

Homeowners insurance will not cover any damage to the homeowner's car.

Homeowners insurance will only cover the carport.

Your car will be covered only by the car insurance.

Two separate issues.

The car port may or may not be covered by your homeowners insurance. The car absolutely would not be covered under homeowners insurance and any claim needs to go to your auto insurance company.