No, the hydrogen breath test and methane breath tests are different from the h pylori breath test. There are 2 different tests.
Yes, it is an Antibiotic and I imagine you're very resistant to taking Antibiotics as am I but this one does seem to be helping a lot of people with SIBO.
Sulfur reducing bacteria metabolize sulfur to hydrogen sulfide. This is a gas and you would have very smelly gas if you had these. As far as which bacteria are sulfur reducing - I don't know but google should turn up results.