A gram stain from a dropping sample can determine if there’s a high amount of gram positive or negative bacteria in the dropping sample. A fecal float is used to determine the presence of parasites or eggs. Without some specific equipment neither is really possible at home unfortunately.
As for vitamins, definitely liquid B complex and I would strongly suggest rooster booster poultry cell because it has a lot of iron in it.
It has E in it but for greatest impact I would suggest getting some E vitamin capsules.
Also a 12 ml syringe for oral dosing because he isn’t going to want to take the vitamins freely, and I wouldn’t blame him, tastes awful.
Iron supplements can cause nausea so I suggest starting with a low dose of the poultry cell if you can find it, around 2ml twice a day and then move up to 3 ml twice a day. It says it can be given in 6 ml dosages but I found out the hard way that that triggers nausea pretty bad in geese and my goose vomited it all over the room when I gave it to him.