OK, thanks for your answers.
1. The flue cap is in place and was replaced 2 years ago when the roof was redone.
2. The vent is pretty straightforward with only a light elbow (see picture). Distance from the top of the tank to the roof is no more than 5 feet.
3. the match test was conclusive. The smoke got sucked up immediately.
4. the tank is in a closet off my garage and no chemical are used around. It seats 18″ of the ground.
That being said, do you think this is a goner or not?
I have added more pictures that show some rust on the top of the tank around the Hot and Cold connections, rust also at the top and bottom of the tank, and rust around the combustion chamber.
Thanks for your expertise.