To answer your questions without digressions:

1) After food runs out, the villagers start to suffer from starvation damage. I think it's 1 point every feeding time or so, but I forget exactly--you can look it up in the log if it happens. A fully healthy villager has 100 health, so under optimal conditions it'll take 100 feeding times for them to pass away (if I'm correct about 1 point per), but of course they also can take damage by researching, building, or from sickness.

2) As everyone above has suggested, start mushroom hunting in earnest. There are about 8 spawn points where a mushroom might appear. Just keep looking around the edges of town and you'll be able to notice most of the mushrooms when they appear.