1)Doesn't matter. There's not going to be enough time for an infection to occur.
2)Yeast will eat sugar and fart co2, no matter how miniscule the amount, look at bread, which is another form of fermentation.
3)Look at bread, which is another form of fermentation.
It's not the time in the oven that matters. More than likely the recipe requires the dough to rest for a period of time...either in the fridge, or at room temp for a period of time which would give the yeasties enough time to do their thing. But it probably wouldn't take that long for the yeast to eat that minimum amount of sugar to do what it needs to do.
The fourth possibility is that the yeast is more meant for flavoring than any co2 production. Or it is meant to rise a bit and give the cookies a bit of an airy complexity.
The other thing to consider though is what the recipe creator actually meant by brewer's yeast. Did they really mean yeast used in fermenting beer, or something else.
Brewer's yeast outside of what we know it as, is actually also used as a food supplement, and is sold in health food store.
In fact this is what it says from an online vitamin/supplement dealer.
In fact often brewers yeast as sold in healthfood stores is often a dead version of it, it won't ferment. It's been already heated or (gosh, if only they knew) irradiated to prevent fermentation, and just provide those nutrients.
In fact in brewing we often recommend folks go get some "dead" brewer's yeast from a health food store to add to the boil as a yeast energizer or to drop in a fermenter to help stuck fermentation, yeast are by nature, cannibals, and when given dead yeast will often get really excited and eat that and everything in site after.
The trouble with giving washed yeast (I bet the recipe was calling for dry yeast unless it was meant to be a "beer cookie" like beer bread,) is that you might not like your cookies, they may taste too "beery" having been fermented already. So they may actually not be like the recipe was intended to taste like.