We have a reverse osmosis system that filters the salt out of our drinking water, so it is possible. It will take a very fine filter. It will depend on the what the other contaminates are on how to filter them.
Unfortunately you bird is quite ill. I don't see any visual signs of her coming back into lay, so I doubt it would be egg binding. Pictures of poop, what type of chicken food she had been eating, and any dewormer or other information of past care would help in knowing what might be wrong.
What is your purpose for getting roosters? How many hens do you have?
Most often when someone is talking about separating the roosters from the hens it is because they hatched or bought straight run chicks and now have to many roosters compared to the hens.
I am not aware of rooster...
Yes, I have had 3 broody ducks on the same nest. Not a single duckling hatched likely because they kept moving the eggs so much. They do not take turns. They either sit or they don't. Honestly you are still at a stage where you don't know if any of your ducks will go broody, nevertheless...
Unfortunately (or maybe fortunately) hatchery quality barred rock don't always get defined head spots for pullets. As long as they are pure barred rock you can still go by single barred for pullets (darker) and double barred for Cockerels. That should become clear in the next couple weeks.
Just bring the humidity up up bit for those still hatching. Manually add water with sponges if needed. It is tough to tell from the picture why the chick didn't pop out. If it was shrink wrapped it would not fluff up. Once a chick starts to zip and stalls it can be assisted.
Drakes can injure chicken hens if they try to mate with them.
Other than that your numbers sound fine.
My teenage daughter is the main poultry tender here, and yes she wants to hatch and keep everything. Each year I struggle with how to handle the culling of some of the males. I have decided...
If you get chicks you will be integrating them with grown hens. It will be the same now as it would be next year. Unless you have a broody raise them. There is no way to know when or if you will get a broody.
The smaller paler comb are normal for a hen that is not laying. Did she take a break from laying during her molt? Any current known stresses that could keep her from laying?
The chicks will be fine in the coop. Chicks that have been raised outside with a heat source are often roosting by 6 weeks. Your brooder chicks will likely pile together for the night keeping each other plenty warm.