Okay, this is going to require some work, *if* you believe this to be a crop impaction.
And you should assume it could be comething contagious just in case.
Is she 'bobbing and weaving' as though hiccuping or trying to vomit? You say she is gaping? She can't vomit unfortunately and this is actually a sign of choking.
Is there any blue on the tips of her comb or tips of her toes (lack of oxygen)?
If she can be handled, this will go easier.
You have separated her, which is great.
If she will eat, offer diced tomatoes or applesauce only for a day or so. The reason you do this is to acidify the crop and soften the blockage, assuming it is fibre or something digestible. If you suspect she has swallowed plastic or twine, she is in a heap of trouble.
It also helps to offer olive oil from a dropper, needleless syringe or straw. Nice if she will take it willingly and if not, you may have to get some help and gently press on the sides of her beak back at the hinge until she opens and lay some oil far back in her mouth, letting her beak go quickly so she will swallow and not aspirate the oil. The oil is used to get the mass moving in her drop.
The next part takes some experience, and you will get a lot of it if you feel you wish to proceed. Give the hen no less than an hour to let the acidic food and oil work around in the crop. It involves crop massage and learning how to pinch the crop safely to break up the mass. Again, this is assuming the mass is caused by something which will not cut her on the inside, so you have to assess carefully.
I'll get back to you as soon as you can answer the other questions and here are some other threads. Be very careful how you proceed from this point onwards, because crop problems can have wicked bad outcomes. If I had had a vet nearby who treated chickens I would have taken mine, but I don't. My girl pulled through after a week of effort several times a day. If you feel you have to cull, I understand perfectly.
