Does a characters armor rating apply only to melee damage or will it also protect, for instance, from a dragon's fire breath even if the armor does not have fire resistance?
Thanks

It only apply to physical damage. Which mean melee/range non-magical

Such as sword, bow...etc

Fire or other elemental are resist by magic resist and elemental resist

So yes breath are magical damage

Physical only, no protection against magic unless you have the "Elemental Protection" shield perk that allows your shield to block 50% of fire/frost/shock magic.