Does an insurance company send an adjuster no matter what size fire and how do they determine how much to award for damage if no one was sent?

For very small loses some insurance companies take the Word of the insured and accept a suitably executed and typically notarized "Proof of Loss". This is a sworn document attesting to the loss. The payment will be made based on repairs, estimates, etc., sent to the insurance company, LESS deductible.

Other insurance companies will send out an adjuster irrespective of the claimed value of damages, especially in the event of fire.