Sounds like it could be temperature related. When it's in the 90's better to not have there crop so full. Which requires less feeding and somewhere cool to hang out. When they're digesting there crop it releases heat in there body. Overheated, chicken will vomit, be lethargic, and stop...
Well since no notice was given to you. You have the right to stay and make arrangements to gather your things and find a new place. Even though they sold the house without your knowledge, there is a thing called renters rights.
Hatching eggs are easy after you study up and get guidance from the members here.
Get motivated and try, it's a great learning experience. Plus the chicks imprint on you instantly.
Technically, you don't need any roosters, unless your free ranging them on your property. Roosters are good for being the alarm in a flock or you need them to produce babies.
The important part is making sure the space is big enough for the amount of chickens you want. This will reduces fights...
Replacement should be females only, since the lone male can survive alone.
Important part is not to put young goslings with an adult bird. Grow them out first. They need to be fully feathered before adding the male to the group. This will reduce major injuries.
Hope that helps.
If the lime looks white, don't use it around your chickens. The white processed version is refined to kill insects basically it's an insecticide.
You can use agricultural lime with chickens it's safer.
Decrease the light level of the nest box area. It needs to be fairly dark so they can't see there eggs. Once they lay they'll lose interest cause they can't see the eggs. Chickens in dark spaces naturally run towards the light most of the time.
Don't use new pullet eggs for incubation, you have to give her a month of consistent egg laying and watching her being mounted successfully, to start incubation.
If the cracked area looks dry, you have to remove the chick before it shrink wrap in it's membrane. When that happens it will die. Use a bright flashlight to see and check the condition of the egg in the incubator.
That fencing photo almost looks fake or rendered. But go with 6 ft.
My tallest fence was 5 ft on one side and 3 ft on the other. My chickens sometimes went over the 3 ft side just to look around but came right back in the yard.