I used an axe. She didn't seem to feel any pain.
I will do an overview of the thread. I feel like people might want to learn from this, and I will write a summary so if people search for an answer to a problem similar to the two I've experienced, they can have a better experience themselves and maybe cure their chickens. I think it is interesting how unique my chicken's problems were, because when I searched for help on Google, no results with a similar issue would come up.
I didn't say their names, but I will now.
First there was Syrup, the hen with the yellow growth in her reproductive tract. I was unsure of what to do with it for the first couple of days. She pooped over it and a day later she had a prolapse with some of the actual tract was poking out along with the yellow blob. Syrup pecked off some of the yellow blob, and then all of it the next day. When I went to poke back in the tract, it was dark red instead of light pink. On the first try, I gave her a warm bath and my glove wasn't lubricated. It didn't go back in. The second try I soaked her for 20 minutes in the warm water (it was kind of hot) and my glove was lubricated with Witch Hazel. I got it back in. It went out again the next day so I repeated the process and it stayed in.
That is the end of Syrup's story. There was no more prolapsed vent and she's pretty happy right now. I think that the yellow growth was not a part of her as she was able to peck it off no problem. If your chicken has a yellow growth and your chicken won't remove it, I feel you should remove it cautiously. She had it hanging there for 5 days.
Then there's Butterball, my currently dead hen. I think this was something set up with her genetics from the start. Over the past 6 months, she'd get more and more blind each day. Her eyes were still a bright orange but her pupil would get bigger the more blind she got. She could recognize a familiar path to the coop, but if you put her somewhere else, she'd be completely confused.
Two weeks ago she became completely blind and that was the start of her problems. She had absolutely no idea where she was and could just barely detect a difference in light. She did not react to the flashes from my camera if I took a picture of her. The few things that would make her happy is to hear other chickens, or to hear her friend, Syrup.
At first, Butterball just stood all day in the coop. I put her in a cage with food and water, but she rarely drank it. Butterball had lost a lot of weight and it's a shame I didn't notice quick enough. She weighed half, or maybe even a quarter of her original weight. I brought her inside, and it seemed like she was about to die 9 days ago. I gave her water mixed with vegetable juice, sugar, honey and all sorts of things. I also gave her oil from tuna cans. She was a little stronger, and I took her outside to go eat with Syrup. Everything was going good until yesterday. I picked her up to go outside and she vomited, I thought that was no big deal because I used to have one hen which did that too and had no other problems. When I brought her inside, she felt cold. I put a towel around her. This was 4 PM. My brother walked in and kicked over the vitamin water I gave her, so instead I just gave her water with tomato juice and sugar. She just kept sleeping since then. If I pet her she would twitch or perk awake. She stopped doing that at 7 PM and seemed to be completely unconscious since, in a kind of dead position.
Then she started stretching her neck at 10 PM, which was her vomiting. The floor by her face was covered in vomit and it was darkish colored. It didn't smell abnormally bad though, just smelled like chicken vomit. I cleaned it up, and after an hour, she breathed normally but then stopped. I gave her CPR (which is foolish, but hey, i'm a kid) and she kept breathing for 15 seconds before dying at 11:55. I was typing a reply, but then at 12:30 AM I heard a cluck, and she was alive and breathing with her eyes closed. She kept breathing throughout the day, even through the morning and did not stop.
She would not eat or drink so I had to cull her.
If you want to prevent the problems I had with Butterball, buy good quality hens, and if you buy low quality ones, make them into stew before it's too late. I will definitely keep that in mind next time I buy my chickens. I will not get them from the local feed store anymore unless I'm buying broilers. You could never foresee this when Butterball was young, she was one of my most active chickens and she loved to eat. She was also strong and was one of the highest ranks in the pecking order. Even when she was blind, the other chickens respected her.
I hope these problems never happen to any of you! I will be getting new chicks next year in March.