I think relaxing a bit more about it all is a good thing

As Davidd has said, often things are fine but novice keeping can make you look for more than there really is.
With regard to the sneezing, I doubt its anything more than that. If they are well, eating, pooping and so on I don't think its anything to worry about. I had one pekin sneezed a lot regardless and she was as fit as a fiddle. I would guess the reason why Baytril and Tylan have not worked is because there wasn't anything for them to work against. I think maybe you just have a hen who sneezes
With regard to the crop problem. I don't think your bird has a problem from what I've read. Her crop is emptying overnight and she is eating, drinking and pooing as normal. So please try to stop worrying about this. I'd also not give live yogurt and olive oil unless there is really a problem (dairy isn't a natural food for chooks is my thinking). I'd say avoid poking it or anything as this could maybe just cause aggravation to it if all is well. Just let it do its thing and check every few days if you must. But if she is feeding, drinking and pooing and bright then try to relax.
The neck/breathing thing could possibly be something (didn't Tim suggest gape worm or something like that) in which case that is easily solved I would think. Also I recall a hen who did this on and off and was never ill and had a long life.
I think the thing to remember is that just because something happens for a short period of time (like the neck thing) doesn't mean its a disaster and something is drastically wrong. Often just waiting till the morning or a few hours will usually see things change and your bird settle again. At least in my experience anyways. The sick birds, as davidd has said, you can tell when they are sick. Listless, head hanging, off their food and drink, poos are funny colour/consistency, eyes go pale, comb/wattles maybe change colour, that sort of thing.
Try to have a bit more confidence in yourself and your birds. As you get to know them and their ways you'll probably start to feel more relaxed about keeping them and won't get so worried about all the little things as you are now.