There are many variations in peafowl but there are no breeds. Your criteria is quite unrealistic although if you happen to develop such a bird the world will come knocking at your door.
If it is cocci it is probably too late to order the toltrazuril but here is a place I have ordered it from before. I order 500ml and larger so I use a different supplier now. Chewy.com may also have it.
The chick will have enough egg yolk in it to survive for a few days, it is not imperative to feed it right away. It will start to peck at most everything soon and find the feed. Dipping its beak in the water is the first thing you should do but feed is not a requirement yet. Put a bright...
This is where you begin your education, https://www.backyardchickens.com/threads/peafowl-sticky-topics-index.389059/
Congrats on hatching your first pea, most people can not.
I have known breeders that completely remove all the perches during the breeding season. I have lots of perches high enough to walk under and some that are adjustable where I can lower them down to four foot for the season. Eggs don't usually break dropping only four feet onto the grass...
There is also different sounds that High Spaldings and Greens make that the IB type doesn't make. One of them is kind of trill and exotic sounding. Look at some of these sticky threads, housing is in one of them. https://www.backyardchickens.com/threads/peafowl-sticky-topics-index.389059/
If you are concerned about noise then you should probably not get any peafowl. Those of us who love peas love the 'noise' and miss it terribly during the winter.
Begin your education here; https://www.backyardchickens.com/threads/peafowl-sticky-topics-index.389059/
Two BS birds will produce BS all of the time, one BS and one split to BS will produce BS about half of the time and two split to BS will produce BS about 25% of the time.
Colors and patterns...
You are very welcome. When I was getting started in peafowl I too was helped out by the very small community here on BYC and is the reason I still contribute helping others whenever possible.
Good job on the chick. The ideal setting is one that allows the egg to lose about 15% of its total weight during the incubation process. Your local conditions are unique to you so you will have to experiment what works best for you. You do this by weighting the egg as you set it and weekly...
Unless the parents are closely related it is more likely an incubation problem. What you are describing could be because of incubator temperature or humidity are off and the floor surface may be too slick. Use the woven rubberized shelf liner for the best results. Find a lab quality...
I have hatched eggs out of yearlings before. Early hatch chicks can be mature enough the first full year, (yearlings). Usually they need a more mature cock to make the eggs viable, yearling cocks can lack the mechanics necessary for successful mating.