I think you should post under Emergencies / Injuries / Sickenss & cures for better & more feedback. I agree with the last poster, the poop sounds normal and it is normal that they don't roost, this is something that takes them time to learn. You might have to teach them. Sometimes they just prefer not to roost. I think this is pretty common with Silkies but it varies from bird to bird.
What are you feeding them and are they eating okay? Have you examined the eyes, mouth, vent? I am not an expert but there are many experts on BYC that will hopefully give more advice.
Sometimes closing their eyes during the day is normal, like when they sit in the sun for a dust bath/sun bathing / nap. But for the most part they should be alert during the day. My main concern is the 'droopiness'. This is definitely not normal. Unfortunately birds do not show symptoms of being ill until they are very ill because as a survival tactic they have evolved to hide their illnesses, so any time they appear lethargic it could be serious. If these are pet chickens and you are concerned for their health, I would take the droopy one to the vet, and take a few poop samples with you (one from each bird to check for parasites). Unfortunately it is not uncommon to see a lethargic bird on one day and then find it dead a day or two later. On the other hand with supportive care they might do fine and you can get lots of advice here on what to do.
I would not give sugar. Chickens are so small that a small amount of sugar would be like us eating pounds of sugar. A little is not a problem.
I would offer them scrambled eggs, vitamins in the water, yogurt and high protein chicken food, I guess layer mash since they are close to the age of laying. I would not worry about vaccines right now, as they would need to be healthy and not stressed for a vaccine to work anyway. You could reconsider this after they are settled and hopefully healthy.