Rain is different, it doesn't pile up white fluff (aka chicken lava) all over the ground.
That said, most of mine hate rain too, so I try to make sure there's plenty of spots they can shelter under as needed.
Completely normal, many flocks hate snow and would rather huddle inside the entire day if given their choice. I shovel clearings and pathways around the run so they can do loops around the run and reach the water and the usual food drop off points.
Both, probably. They get into habits that can be hard to break unless they want to, hence why I'm a little more persistent about getting them to roost compared to some folks.
Having extra artificial light while they're still getting used to the idea of going in at dusk will likely help at this...
That is a lot of scratch. Assuming they're eating 8 cups of feed, 2 cups of scratch is 20% of their intake. Treats should be kept under 10% of intake as excess fat in chickens can lead to laying problems and fatty liver disease.
They do not need light at night and I'd discourage folks from leaving lights on all night, as animals sleep better with darkness. They do however need enough light at dusk to see, in order to get up on the roosts.
If you are using a battery operated light in lieu of windows, turn it on about...
You didn't mention light and I don't see windows. Have you walked inside and shut the door at dusk to see how dark it is inside? They can't navigate if they can't see.
Were they roosting reliably in your previous coops/set ups? Have they ever roosted in this coop? Did you home them to the...