if you have home owners insurance or if there was any other damage to your home it should be covered by your insurance. i had a wood burning stove that caused my house to catch fire so all that the stove damaged (including itself) was covered by my insurance.
Likely the damage to the furnace itself is NOT covered, but any ensuing damage - water damage from the fire department to the house or contents, or smoke damage to contents, WOULD be covered.
yes, your furnace, and any damages to your home would be covered under your homeowners policy, less any deductible you have on your policy. Contact your agent for specific details. Sorry, hope things are better for you and I hope no one got hurt.
This all depends on what caused the fire. If the fire occurred because the furnace was poorly maintained, then the damage to the furnace would not be covered. If it was due to another cause that is an insured peril (if you have a Named Perils form) or is not specifically excluded (if you have an All Risk form), then all damage would be covered.