Your hunch is right about the first hunt, you are allowed to mess up a couple of times so don't worry if you are wrong about your first guess. As for feeding people, they only accept prepared dishes, not raw ingredients, so you will need to cook some food first.
Well just having the ingredient in the dish might not be enough, if someone was looking for an egg dish and you gave them a cake instead that probably wouldn't be what they were expecting. Some girls are more picky than others and there are more dishes that get unlocked the further you get into the game.