Home insurance isn't mandatory, but most banks require you carry home insurance before they approve your mortgage.
Easy ways to lower your payments include: smoke detectors, using non-flammable building materials, fire alarms, home security systems, heavy duty locks, video monitors, fire proofing the home, etc.
In most cases, the insurance company will hire an independent appraiser to assign a value to your home. They will use that number as a benchmark when determining your rates.
Flood insurance is a separate product and needs to be acquired separate from your home insurance policy.
Typically, home insurance covers theft of all kinds, though each policy will have different limits and details.