For the older heater, go here: http://www.waterheaterrescue.com/Longevity/inspecting-a-water-heater.html and do the external inspection. If you can, photograph the combustion chamber, trying to get pictures of the top and sides and post them here and I’ll tell you what I think. It IS a very old heater, but sometimes those can still be in good enough shape to keep going.
For the newer heater, get SKU25, here: http://www.waterheaterrescue.com/OrderPages/Power-Anode-For-Combos.html .
Regarding the black stuff, does either heater have braided stainless steel flex lines? Those have a rubber lining that has been known to cause this problem.