What's her poop like? Any photos?
I agree, it doesn't look too good. Marek's still comes to mind.
Interesting that feeling under her vent between the legs that she passes gas. I've never had that happen.
Her crop is emptying, no lice/mites. Can you take a fecal float to check for worms...
Welcome To BYC
I'm sorry that your hen is not well.
Can you post some photos of her and her poop?
Can you feel her abdomen below her vent between her legs - is there any bloat or feeling of fluid?
Has she ever been wormed?
I'm not sure what's going on with her. You are doing...