I always recommend you keep as few roosters as you can and still meet your goals. That’s not because you are guaranteed problems with more roosters, just that you are more likely to have problems. I don’t know your goals but I can kind of guess. I think you are going to free range them and you want hatching eggs.
A Turken is a chicken. Breeds are a manmade thing. Chickens will mate with a chicken regardless of breed. I’m aware of a couple of fatal genes, genes that if they pair up they will kill the chick. The Frizzle gene is one but you don’t have that. The other is the rumpless gene that Araucana have. If your EE’s don’t have a tail then they probably have this gene. If you cross a rumpless chicken with a rumpless chicken then about 25% will die before hatch.
The Turken naked neck gene is not a fatal gene. It is dominant so any chick that gets it will have a naked neck but a Turken can mate with a Turken without a problem. They will mate with any chicken.
You’ll get different opinions on how effective roosters are in protecting their flock. Some will sacrifice themselves to give the flock a chance to get away but the vast majority of mine tend to lead their flock to safety once a true danger has been identified instead of sacrificing themselves. I’ve had two separate dog attacks where I lost several chickens. The dominant roosters survived both those attacks without injury. What they are going to do will depend on the personality of the individual rooster. With your breeds I think it is just luck with what they will do.
You do get some protection from roosters though. They tend to be good lookouts, watching for threats. They are more likely to see something coming than a flock without a rooster, though often a dominant hen will perform the same lookout duties in a roosterless flock. Each chicken, rooster or hen, is an individual and you can’t be sure how they will behave.
Another advantage to a rooster is that a rooster will usually check out something suspicious. If they see something suspicious they will normally position themselves between the flock and the perceived danger until they determine if it is truly a threat or just something that can be ignored. This is a trait I like.
A rooster may be able to defend against something small and live through the encounter, maybe a puppy, cat, or small hawk. But any major predator will make short work of the rooster if he tries to fight.
Bottom line, you can’t be sure how any of them will react until they are in that situation and that is an individual thing. Don’t pick a rooster for defense based on breed.
I’m not a believer in magic ratios of hens to roosters. You can have the same overmating or barebacked hen problems with good or bad hen to roster ratios. There are a whole lot of different factors involved. The hens have a part to play as well as the roosters. Many breeders keep one rooster with one or two hens throughout the breeding season without these problems. People with one rooster and over 20 hens have these problems. The worst time is during adolescence. They mature at different rates (cockerels before pullets), hormones are running uncontrolled and wild, they don’t have good technique, pullets don’t cooperate so the cockerels use brute force, good technique is totally unheard of, it gets pretty wild and wooly with adolescents. Most mature hens and roosters behave quite a bit different behaviors but on occasion you get a hen or rooster that seems to never mature.
Occasionally you get a hen that has brittle feathers. No matter how correct his technique the feathers just break. It’s usually a nutrient/genetic thing. If they all have brittle feathers then it’s a flock nutrient problem, but if it is only a very few then it’s much more likely that genetically the hens can’t process those nutrients correctly. When you see a problem it often helps to determine if it is an individual chicken problem or an across the board flock problem before you decide how to treat it. When I first started out here, my first flock was one rooster and eight hens. Two hens developed bare backs so I ate them. With a much worst ratio, 6 to 1, the bareback problem went away and never came back in future generations.
Two young viral active roosters should be able to keep 3 dozen hens fertile in a free range situation. Three is certainly a reasonable number and it could help to have a “spare”. Instead of worrying too much about breed, keep the ones that look and act like you want the chicks to look and act when they grow up. I tend to keep the early maturing cockerels too since I think they make the best flock masters.
Good luck. Sounds like you are in for some fun.