Re: Blackhead: they catch it after ingesting a worm that carries the disease. The worm cysts can live in the soil for quite some time. If you just google 'blackhead' you'll find a concise explanation somewhere. I've always kept my chooks with the turkeys. I advise you to persevere against blackhead, like I did, because in about 5 generations or less I bred 100% naturally immune stock, and never had a problem with it again. The immune stock were hatched and reared in the midst of the dying older siblings, on the same land... Along with all the chooks. I never used medicated feed, though, which usually compromises livers as most antibiotics and meds do.
If they get blackhead, the cure seems to be: (this works for 99% of cases but there are different strains of blackhead, some more virulent than others, so not a guarantee since I don't know which variety I had): get a cupful of fresh raw unheated milk, not treated in any way. (I used cow's milk). Let it sit and skim off the fat that rises to the top after an hour or so. Then add a flat teaspoon or flat tablespoon of honey, preferably raw and untreated, to the cup, mix it, and give it to the turkey that's ailing. Important: wait until the bird has been refusing food for at least a day, and the poops are liquid and bright yellow/yellow & khaki. This is close to liver failure, and the disease appears to have run its course at this point, and the milk and honey will have the bird on its feet in 24 hours. If you give the milk and honey unskimmed or too soon in the illness, the fats will kill the bird or prevent the cure from working when it's administered at the right time. I wait until the bird's lying down, because that seems to be the right time; you may have to dip its beak in the mix so it tastes it, but most will guzzle it as soon as laying eyes on it. Generally only one cupful is needed, but I'll sometimes give a bird all the cups it can drink in 24/48 hour period; some birds go down fast, in days, others go down for weeks. Cereal grains like wheat and corn, etc. are to be avoided; millet and oats may be ok.
Re: turkeys under hens: I advise it. Turkeys can be terrible mothers and turkey babies can be blissfully ignorant about the world around them, and being raised by a chicken hen, preferably with at least one chicken 'sibling', will make them worlds sharper and wiser, better foragers, etc.
Raising chicken babies under a turkey hen doesn't work so well. They'll abandon her for a fool, she'll get distressed that they don't need her, eventually she'll start showing minimalist care of any bubs she hears making chicken noises. At least in my experience.
Re: feeding: I wouldn't advise giving chook feed to turkeys because they won't do as well, and some chook meds are toxic to turkeys. The turkeys will need more protein, but they are primarily green feeders so will always do best when getting their protein from insects and plants, rather than meat byproducts. The best feed for baby turkeys, which put an end to Tuberculosis in mine, is hard boiled eggs with dandelion or onion/garlic, raw and finely chopped.