If only three frames of bees, I would reduce the space in the hive to one box. I would add a fresh pollen patty and some syrup since they are too weak to forage themselves. And I would do a alcohol wash with some of the bees on the brood...,make sure not to get the queen A good count is 300 bees. Count the bees and the varroa. Until you assess the varroa and reduce the hive, I would not add a frame of bees from a healthy hive...basically money down the toilet then. As well reduce the entrance to reduce the tendancy of robbing from the healthy hives.
Asses the laying pattern of the queen, and assess the amount of drone brood to the amount of workers. How old is your queen?
To do the wash, you need a jar with alcohol and bees. Shake vigoourously for 8 minutes or let sit for 1/2 to 1 our then strain the bees from the liquid with a mesh strainer big enough for the varroa to pass through. Count and divide and get a percentage
Oh yeah, sounds like at one point the hive had nosema. If they are not eating the syrup, you still have nosema. You will need to feed them fumigillan b somehow. IF you use the pail feed method, your hive must be out of honey production and you need to reduce the entrance of the hive to keep robbing at a minimum.
Another method to feed fumigillan is to drench them. Which might be a better option at this present time. It requires three times once a week. About 70mls of mixed syrup and fumigillan per dose. Drench the bees and the frames. They will clean each other and injest the medicated feed.
Bees with nosema are less prone to injest any feed since nosema infects the gut of the bee.