Any new dog is going to be a real risk to your chickens!
You did pick a sweet guy, who hasn't had a good life, and he is going to be a challenge. This is a marathon, not going to be fixed in two weeks, so TRY to relax and think LONG HAUL, but worth it.
Every interaction is a training interaction! He's smart, stressed, and looking for direction, and that's you. He's also, if actually the breeds mentioned, going to have that very high prey drive, and very high need for exercise, and walking on lead isn't enough. Too bad you don't train for marathons! A tired dog is a good dog...
Actually, if you do have a friend who runs, maybe they would like a running buddy, and could take him out for you. Dog parks, maybe, but they can be danger zones, especially with a new dog who's not really bonded to you yet. And off lead except within fencing, no way!
One of my rescue dogs couldn't be crated either, and we had to literally chain him to a metal post in the garage if we left him alone, until the house training was good.
It can be possible to crate train through this, and deal with the separation anxiety so many rescue dogs experience, and it often takes meds with the retraining to work. Your vet is a resource here, and if there's a veterinary behaviorist available, find out!
Mary