I am not an expert in traditional fermentation but I believe presence of contaminants depends on the crop, the strain of yeast present during the process, and conditions. So basically it can vary a lot.
Methanol and other byproducts do vary based on strains, conditions, etc. Generally, methanol is not an issue in things like wine because it's not produced in large enough quantities, even when conditions are poor. A treatment for methanol poisoning is actually ethanol (and likely some NAC). Only when distilling is methanol concentrated enough to cause problems. When done correctly, the distillation process separates the methanol from the other distillates at specific temperatures. Usually the heads and tails of a distillation run are thrown away. I believe it's the head that has the lions share of methanol.