Well, I know this is an old thread but since there aren't any answers I'll answer it in case you're still here, or someone needs it.
1. Some of the stews are actually quite useful!
One stew can completely restore villagers' health!
And one is used for one of the puzzles
The gong piece at the bottom of the pond
Make one of your villagers eat the stew (EDIT: This villager must be at least 14 years old and doesn't dislike swimming), it should say "Strange stew...your villager feels no need to breathe!" Immediately drag that villager into the pond, they will be at the bottom of the pond for a while and return with the gong piece.
2. I'm not sure, sorry! Although I had a kid who gained building skill after exercising (by eating the exercise stew), so I imagine it could be possible.