A. Antibiotics cannot be given without your veterinarian supervision and prescription.
There are some oral solution with chlorhexidine and zinc you can buy over the counter (Hexarinse Oral Rinsing Solution for example). Unfortunately it is only a treatment trial and probably they won't resolve the problem completely.
Gengivo-stomatitis in cats is often immuno-mediated and requires steroids and sometimes dental surgery. You can find good sources of informations about the disease here: http://www.vet.cornell.edu/fhc/Health_Information/Gingivostomatitis.cfm
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