HI,
I'm pretty new to ducks but brand new to Cayuga. Got 5 of them. I know that they can have a bit of yellow on the stomach and that's normal. As they age they actually turn white, rather than black, which is really interesting. Perhaps you got a "crested" cayuga if there is such a thing?
What I've found about mine, compared to the Welsh Harlequins I did have is that my Cayugas seem to be much more "trusting" once they know you. So, basically, when I walk up to them they don't run away as fast. lol. they are more likely to come eat from my hands, let me pet them, They are easier to catch but don't like being held as much. They seem to really like the water. I have mine in with chickens - all the same age as them. At first the ducks were actually mean to the chickens (i figured it would be the other way around!) but I think it was more out of fear of "what the heck is that weird thing with a beak" rather than actual aggression. But as they're together more and more I find they really tolerate the chickens just fine.
Ducks in general don't like to "return to the coop" because they don't have a roosting need. They prefer to sleep outside rather than inside. They prefer the cold and rain. I find that what works best is to take away their food during the day. They can eat what they free range but withhold the actual grains. Then, at night I clink on the food and it took my last ones all of 2 days to figure out that meant "time to eat! time for bed".
I find my cayugas to be very quiet as well... They are still just babies so only time will tell but I hear they are quiet, in general. My WH had to be rehomed because they were SOOOOOOO FREAKIN' LOUD. It was like I had 10 geese!
One thing I will say is that ducks are SO MUCH MESSIER compared to chickens, when it comes to water. Either way, they are messy but go to your feed store and invest the $20 in the hanging water nipple feeders. They are worth every penny! The ducks are so inquisitive they will naturally go to "peck" at the nipples and quickly figure out that there's water. My WH and Cayuga both figured out the nipple waterer within minutes. They get enough to wash their throat and their nostrils without issue. I make sure to also just give them a little pool of water - usually a large bird bath top or a dog bowl type deal of fresh water so they can truely clean them selves and clear their nostrils out. They really enjoy their treat. I found that with a big "kiddie pool" my WH were loud because they wanted the water changed out (several times a day), or it wasn't clean enough for them, or it got too hot in the sun or WHATEVER. I found with the smaller baths they use it up, and so I replace when I go visit them. But, that's up to you - I know a lot of people have great luck with kiddie pools if you have enough property that you dont' care about ducks quacking super loud. And who knows if the the cayuga would be the same way?
I hope this helps a bit?! Oh, and I did notice that for some reason their feathers get much more "weighed down" when wet so if you do want to give them a bath as babies make sure it's very warm water and keep an eye on them because they do get "water logged" easier than other breeds.