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.
Can you reach your birds when roosted? Catching can be easier at night.
We hold chickens during the day without issues. Once caught hold the wings down with firm pressure and hold their body against yours.
Hens can hatch and raise chicks in any weather. The colder it is the harder it can be on the people providing a constant chick safe water. When in February did she go broody? If it has been setting less than 2 weeks she will likely sit through to hatch.
If she has already been sitting more...
Only sitting on nests during the day could be due to lack of space, or roosts, bullying, illness, or the start of broodiness. If it is for only a couple hours it is just laying routine. If they don't sit on the nests at night do not give them eggs.
Where did you get the chick? It will help narrow down the possibilities. The color of the chick when grown will likely be mottled with possible what I call reverse barring.
I candle eggs that are being sold or given away. I can see hair line cracks that I don't notice otherwise. Rarely I find an odd dark spot, but it happens. We do have several roosters, and frequently have broody hens. I have caught a few eggs that were left under a broody more than a day.
We don't worry about cleaning the yard. Nature takes care of that (a smaller space might get more of a build up). If needed kids can be cleaned. As @Altairsky alluded to when you see kids and animals running free together it is not because there is not poo, it is because no one is worried...
You will find all kinds of advice if you look up what to do with an aggressive roo. Your Cockerel is just reaching maturity and has just shown he is human aggressive. My advice would be to get rid of him immediately.