I can't speak for vaccinated or heavily medicated stock as that can prevent the natural formation of normal defenses against disease, but I would assume as adults your turkeys would be immune to coccidiosis. Mostly adult birds have been exposed and conquered it, though some weakly ones can still die of it if never properly immunized to it. Garlic's a natural immunizer. I would always give garlic as a first line of defense, for all ages, for many diseases and infections, I just give it raw or in granulated form, in their food or separate, however suits you.
I don't think you or other forms of livestock can catch a turkey's TB but diseases are adjusting to every modern treatment and changing genetically so who knows. Transgenic wonders occur.
With dandelions, they eat the leaves, it's a powerful liver detoxifier and support, and the liver is the main organ you'll find to be weakly in turkeys. That's what fails them under blackhead attack, and it plays a role in TB. Egg can be hard on the liver due to high sulphur content so raw onion, raw potato or raw dandelion is an important addition. Garlic's high in sulphur too but I let them eat it as much as they want, and I've never lost one to sulphur poisoning, as some people worry about. The egg just grows them well and the sulphur, balanced out by dandelion, will permeate their flesh and make it fairly impervious to parasites and diseases. I give garlic raw and finely minced to the newly hatched chicks as part of their first feed, and keep doing that for the first week at least, and also give it as a regular staple to birds of all ages and destinations; in fact if they're definitely going to be eaten by us I make sure they are well stocked on highly healthy feed, since that benefit transfers directly to us.
With the egg and dandelion, they want that mainly between the ages of roughly two weeks to eight weeks, or so, and they'll wean themselves off it when they're ready to move onto a more plant-based diet for their protein needs.
As for broody hens, it depends on the hen, really. In the case of turkeys, as well as chickens. (I'm not sure which species of hen you mean). If the mother bird, regardless of species, was allowed to raise the hen naturally and not overly distressed by adverse human interference, she'll likely do great. If she was raised separately she may need practice. I prefer to raise them either with a chicken sibling or under a chicken, because they tend to be less aggressively protective and better at foraging for insects, and the adopted chicken sibling helps wise the turkey bubs up, an it's good to foster cross-species tolerance. If you keep them in a cage for as long as you're planning, you may need to take precautions against the mother turkey trampling them, because they're mainly green-feeders and if used to free-ranging, they can be desperate to bring their bubs out to the greenery, and spend all day pacing up and down the mesh, heedlessly trampling babies. I make a leaning cage wall or put something in the way to prevent that, if I have to cage them, but it's best for their health to eat mainly raw fresh greenery, especially grass. Generally easiest to rear them under a chook hen, though the turkey hens may resent that. They'll know, sooner or later, that you are the one taking the eggs or bubs, and unless they're especially stupid they will identify that the chicken babies and turkey babies are different, and they will try to steal back their babies from a chicken hen, and get really distressed.
There'll be different diseases and different strains of the same diseases where you live, in another country, and the fact that most people use antibiotics means the diseases will be so much more powerful than if people had only used the natural fixes. In the UK, I believe, there is a particularly nasty strain of blackhead. With turkeys, you can expect to lose many, and hope for the best. Birds bred and born for generations reliant on artificial surrounds and feeds can become useless in a natural surrounding, intolerant. If you've got cage-breds and you transition them to outdoors, expect a bit of a trial by fire. Anything your chooks are carrying that never even made them sick for a day will have a go at your turkeys. They take a few generations of hard work to get tougher if bought from a more commercial type of situation. Best wishes. Sorry for my usual overlong reply.