I can't speak to the showing side of the questions but to the growing side of the questions I can assist. I'm new to backyard laying hens but I am not new to meat animals and livestock. yes broilers can be housed with other non-meat chickens but obviously you want to be careful if you have any pests or diseases or viruses dormant or recently in your flock so that you don't have to medicate birds you're going to be eating so with good biosecurity it's perfectly fine to mix them. Also mixing does create some stress for your laying hens because when you remove and process those chickens you're resetting the pecking order again and it doesn't make a ton of sense to constantly do that but if you're only doing it once a year again it's not the end of the world. If you have the space it's probably better to keep them separate but it's not a deal breaker by any means. The feed question is answered by what your goals are if you're looking to get to processing weight as fast as possible and have the fatest chickens then I would feed them a meat bird or finishing feed from day old until processing day but if you're not in a rush to process them and are fine with some slower growth they absolutely can eat everybody else's feed but I would still finish them with a finishing feed for the last couple weeks of their life.
