Seems to have more than one thing going on. How old is this hen? If you said, I missed it. Seems to be a hatchery BR hen, not a young one, either, from the looks of her. The head snaking movement means the crop is probably becoming sluggish, which is more often than not a sign of system shutdown. They also do that when they have something caught in the throat or the crop is full and blocked, not necessarily because of anything specific she ate, but because the crop is simply shutting down and ceasing to move food through. I have an almost 7 year old Brahma hen who is having those issues, but she is nearing the end of her life and it seems par for the course, the crop issues at that stage. I once had a hen eat a frog that she had trouble getting down into her crop good and she needed massage and oiling up for a day or two to get that thing moving along. She did the neck movement a lot. She may not be eating because she realizes food isn't passing into her stomach. Hard to say since I cannot feel her crop and neck for myself.
The lump can be just fatty tissues. You're seeing it so prominent because she is molting and it sticks out like a sore thumb. Sometimes, during molt, many feathers ball up inside and make a mass under the skin. I have a hen who has a smaller lump, been there for a year, but a vet of a friend's that I spoke to over the phone who saw a photo of hers said it could be fatty tissue (yes, he is very familiar with chickens). The lump is still there, not causing any issues. Or it can be something else, an abscess of some sort. Hard to say unless you use a sterilized exacto blade point and carefully puncture the surface of it to see if you get clear fluid or blood.
Also, she could have egg issues, but that lump may not be related to that. Almost every hatchery hen I ever owned died from EYP and/or internal laying, including the BRs. Seems normal for them, sadly. I had one hen whose giant egg-within-an-egg dropped into her abdomen, but the only way I knew was that her belly was hard as concrete and she was losing weight rapidly. There was no bulge, in spite of the humongous mass in there. Those masses you see like that are rarely eggs.
You can't fix oviduct cancer or EYP or internal laying. EYP could be treated, IF you knew a hen had it, but you never do until you see end of life symptoms. It's bad genetics. My breeder hens just don't suffer from that stuff like hatchery stock. My advice would be to stop buying hatchery stock and get better stock, or you'll continually deal with this nasty stuff. I'm very sorry, been there numerous times, but that Brahma I mentioned is my last hatchery hen. She's outlived every other one, but hasn't laid an egg in over a year and is showing her age badly now. The others, my originals, all died off, and the couple that didn't have EYP/Internal laying died from cancer.
