Most times I never know exactly what is going on with a very sick chicken until a necropsy can be done after death. Mine have always been done at home. There are good videos of vet necropsies where the organs are labeled, and you can post pictures here for advice and opinions. First though, I make sure the crop is emptying after not eating through the night. Weird neck movements can be crop-related or may be a neurological symptom. I worm chickens to make sure that a crop issue is not a problem. Poops can give some clues of general health. If they refuse food and water, that is a big problem. I coax them and baby them, but I usually do not tube feed. But you can do that if necessary. Some use antibiotics when nothing else helps, but that may not be helpful if there is an egg laying problem. I have lost quite a few at your hen’s age. Sorry for the loss of the others. I hope that you can save your hen, but it doesn’t look hopeful.