You might want to stop by the Toyota dealer’s parts department and ask for an “exploded view” diagram of the evaporative emissions recovery system (vapor recovery). I no longer have access to technical data, or I’d be happy to look it up for you.
It’s hard to say without looking at the car, but I suspect the black residue coming from under the hood is simply oil seeping past the tired valve cover gaskets and burning on the exhaust, the rising fumes depositing carbon. In that engine I believe that intake is foreward of the engine and the exhaust manifold aft, so the fumes would be coming from that spot. I suspect they’re unrelated to the deposition above the gas door.
As regards the gas door blacking, are there any rot holes around the fill pipe and what shape is your exhaust system in? Is it possible that exhaust fumes could be coming up behind the gas door and leaking out past the upper edge of the door?