Not everytime. I've had a couple playthroughs where it never spawned. I've had one where it spawned in the first store (this was an expert play through so I don't know if that makes a difference or not). It's unpredictable.
And so far I've NEVER seen more than one spawn at the same time. But it is cool to imagine the survivors with two of them.
I've never made my own stock but the only soup I can make that doesn't come out of can or soup mix is a broccoli and cheddar cheese soup. Mmmm, yummy.
Well that's not entirely true, my favorite way to get rid of leftover chicken is to cube it and make chicken soup with lots of fresh veggies. My shortcut is I use chicken flavored ramen noodles as the base