I never saw pics of the mouth fungus. From what I have read the Tetra product your are using it's an old formula, stains plastics and has mixed reviews.
The guy who runs aquarium coop claims that he uses a combination of meds for all new fish he receives. You can look at this here:
As he states, combining meds can be risky but he claims that has has found this combination through a long trial and error process.
If you do something like this the tank water should be clear of the other meds utilizing time and partial water changes.
No carbon should be used during any of this process. Water should be tested regularly as the BB may be compromised already and with all these meds. You need to make sure ammonia is kept low or zero. If high ammonia use Prime. In fact I recommend using Prime period to treat the tap water.
HITH/ HLLE and the pitting you think you see are caused by bacteria but the route cause is that the fish is stressed.
Since the fish has not eaten for quite some time it may be too late but I guess you could give it a try (especially if the Tera med is not working).
Just be aware that this is a shotgun approach.