IMO, you'd have to try real hard to produce enough methanol in your beer for it to be an issue. Even then you'll probably fail more often than not.
Wine, cider or other, probably the same, but I don't know.
Distilling might be a different story. But also a different forum.
As for what happens to it, you drink it. But like many other things that can be toxic, like ethanol, you don't consume enough to be at a toxic level. Though as a teen I tried hard to drink myself silly.