My one note about worming is if you want to do it more consistently then you need to switch up what you use to worm. This is so the worms/parasites don't develop a resistance to it. I personally don't deworm mine and they don't have any issues. I will only worm if I need to.
Could the ventilation fan be introducing a draft accidentally? Also make sure there isn't any humidity as that can also increase the risk for frostbite.
There is no need to a heater in the coop and it tends to do more harm than good. If you keep a heater in the coop and it fails one night, it can be detrimental to the chickens as they will be reliant on it to keep warm that if the outside temperature is much colder than the coop was thanks to...
She is almost constantly looking up? It does seem like wry neck is a good possibility. Give her the vitamins Wryop Rock recommended. You will need to stick with it for a few weeks and give it to her daily. You will not see progress instantly but keep giving it to her.
It is a weird time for them right now when it comes to laying. I would wait until the days get later.
You can also check their vent to see if they are laying. Here is an article I found talking about this with examples and how to check...
When you first put them out in the coop they need to be taught to sleep in the coop. This means coming out right after dark and placing them in the coop (and locking them in it for the night too at times). They will learn to sleep in the coop after a while. For the roost, they will also learn...
It might be the barred rock or columbian rock. It think it is on the lighter side for the BCM. I know for a fact that this is too dark for a buff orpington as they are light in color.
However, a disclaimer is I've not owned these breeds (aside from buff) so this is me just comparing the egg...
The broomstick method is one way. Some do the cone method but that is better when processing broilers as it is more efficient. You just want a quick and painless death.