The water heater is located in a closet that used to be a garage, which they changed into a bedroom. The closet is 10x4 and does have 2 vent pipes for combustible air, one is a couple ft from the overhead and the other comes down to about 2ft from the floor. They both vent into the attic about 3ft from the furnace. Is the corrosion from improper venting and the burners on the furnace have corrosion with irregular flame?
The corrosion in the furnace may be from a leaking A-coil drain line which is a pretty common source.
I see corrosion like that on furnace burners a lot. Often it’s the refrigerant line not well sealed and condensation is dripping into the cabinet. Address the problem, whatever it is. The burners themselves are probably fine.
Water heater looks like it could use a plumber to check it out. Probably old too.
I would be more concerned about the gas fired water heater being in a closet off of a converted garage, made into a bedroom. A double bozo no-no!
Beat me to it! 
Just barely!