yes
Fire and lightning
Each company has several different policies and each policy can cover different perils. Also, each policy can have additional endorsements which would cover more perils than a regular "bare bones" policy. A fire policy is another name for a homeowners policy. The common basic perils are fire, storm, and theft.
Your homeowners insurance should cover damage to your sprinkler system if the cause of the damage is covered by your homeowners insurance policy such as fire, lightning, freezing of pipes, etc. Homeowners insurance is not a maintenance policy and will not cover mechanical failure of your system.
Following What?
It has to be a covered item on your home insurance policy and would have to have been damaged due to a covered peril such as lightning, wind hail, fire, etc.
Any building property policy such as a homeowner policy or commercial property policy will cover fire damage.
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.
A fire insurance policy covers "Fire". That's why it's called a fire policy. If you want more coverage then you have to step up to a homeowners insurance policy so you can get all the other coverages you want or need.
No. Your Homeowners insurance is "Property" insurance. It covers property damages caused by certain covered Perils such as Fire, Wind, Hail, Lightning, Fire etc. You will not find coverage on your Home Insurance Policy for death or related expenses.
No. Mobile Homes are covered under their own Policy. Not under your Dwellings Policy.
No, I'm afraid not. You see, an insurance policy covers items damaged by a covered loss. The covered losses are things like fire, windstorm, lightning, theft, water damage, weight of ice and snow, etc. Nowhere in your policy will find that an items is covered because you forgot to pick it up when in a cab. This is your fault and not a covered cause, so no the insurance policy will not cover it.
Your HVAC is covered under your homeowners insurance for the same perils as your home, such as Wind, Hail, Fire lightning etc and subject to the applicable deductibles. See your Home insurance policy for schedule of covered perils.