Hi,
Sorry for your frustration.
Feather picking can be caused by several things, but the two most common are a lack of protein and overcrowding.
Adult chickens should have 4 square feet per bird in their coops, and 15 square feet each in their run. Less than that, and boredom, anxiety, etc. can set in.
You can either supplement protein every day or every couple of days, or switch to an all-flock with 20% protein, then supplement with oyster shell on the side. We feed everyone here, chicks, chickens, and ducks, Kalmbach's Flock Maker crumbles.
Vent gleet usually is a whitish yellowish discharge from the vent that stinks. If you really believe your hen or hens have that, get some Monistat or the equivalent, and after bathing and drying their beehinds, smear some of that on their vents and give them a small amount, like pea-size on your finger, orally. Do this a couple of times a day for three or four days and that should take care of it.
I'd get some probiotics for their water. Hydro-hen is one, but there are many. Kalmbach's makes one called Lifeguard which is crumbles that can be mixed into their feed. You could also give them each about 1/4 cup of yogurt, Greek yogurt is best, per day for a few days. I'd do the probiotics in water or feed a couple of times a week to prevent it from recurring. Plus, that balances their flora and helps their digestive tract.