Yes, you are correct. Items in your vehicle that are damaged in an accident or fire or whatever are not covered by you auto insurance unless they are part of your vehicle. The alternative is that they are covered on your homeowners insurance. The downfall to this is that you will have a deductible on your homeowners insurance that you will have to meet first.
Carpet DamageYes, if it was damaged due to a covered peril under your policy it will be covered.
If damaged due to a covered peril such As Fire, Wind, Hail, etc,, yes it's covered subject to your deductible.. If damaged to due to wear and tear, No, it would not be covered.
If your air conditioner is not operational due to age, wear or is simply broken down it is not covered under your homeowners Policy. If it was damaged due to a covered peril such as fire or lightning then it should be covered.
Homeowners insurance is a "Hazard Insurance" It covers your property from unexpected "Sudden Losses" that result from covered perils such as, Fire, Wind, Hail, Falling objects, Theft etc.
NO, Your homeowners Hazard Insurance Policy does not pay for maintenance or other home upgrades. However upgrades should be reported to your insurer as they can be covered if damaged or loss occurs from covered peril on your policy. If your Insurer is not aware that you have added an HVAC unit it will likely not be covered if damaged.
Homeowners Insurance Covers the property detailed under your policy. Trees are not an insured property. If a hurricane blows a tree into your house and damages your home then the damage to your home would be covered but if only the tree is damaged then the tree itself is not covered.
Yes, If the system was damaged by a covered peril and can be repaired then thats what the company will do. If it can not be repaired or of the cost of repair exceeds the cost of replacement then they will pay for replacement.
Cell phones are covered as are any other contents if damaged by a covered cause such as a fire. The problem is that all homeowners policies have deductibles. It is not adviseable to make small claims on homeowners policies. They are made for large issues such as a fire or other large claims.
I believe in most any situation that carpet damaged by a dog will not be covered. Of course it will depend on the actual policy and what happened but in most if not all cases this type of damage would not be covered.