Unfortunately, I'm convinced this is a false claim from the manufacturer. There are several threads on here that show thorough testing of this concept, and none of them have been able to show a reduction in ammonia or a conversion of it into a safer form.
False. There are definitely other options for treating ich, but results may vary. One such option-wise chloroquine phosphate, but that's VERY tough to get your hands on.
There are also non-chemical methods to treat ich, such as the tank transfer method which use the parasite's lifecycle against it.
Also hyposalinity, but I think you know that

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This question can elicit a good amount of differing opinions. I left mine off while cycling, but I am not sure it is going to be bad if you run it during a cycle.
I had to look up what that was, to be honest. It seems to be an absorber that can absorb ammonia among other things... I can see too much of it being a bad thing, but only because too much of most things is usually a bad thing.
I think you are too focused on your ammonia concentration. It's really easy to make a blanket statement like "any ammonia is toxic, and therefore you should never be able to detect it." It's much harder to do this when your biofilter is compromised. Just watch your fish for signs of ammonia burn. You will 100% know when it becomes a problem.
This is 100% true. The best way to keep these situations from happening is chemoprophylaxis. All my fish go through QT. It's just not worth the risk.