There is a difference between “wet” shavings and “damp” shavings. People who use the deep litter method, where the goal is for it to compost right in the coop, will tell you there has to be some moisture in the bedding for it to work. When things are too dry they will actually mist the bedding on purpose. The rule of thumb is if you pick up a handful and squeeze it you don’t have any water dripping out, and little to no clumping. So it is ok to get a little moisture on the bedding, just make sure to have plenty of ventilation and keep it turned/mixed up. The chooks will help you with that last part, especially if you throw a handful of scratch or mealworms on top.
You have to remember that my husband does commercial refrigeration for a living. We have three rows of plugs in our barn. One row is wired into a thermostat that is set for them to only be hot when temps are above 85. Another row the plugs are only active when temps are below 40 (for heat lamps, etc). The third row is hot all the time. He gets either digital or manual commercial thermostats that he wires in. But if you Google it you might be able to find thermostats that you can just plug into the outlet that have a receptacle you can plug your fan in to.
When I ordered mine I talked to them and was told you could get all five of one “breed”, or one each of five different breeds, or anything in between. Almost all the breeds they list in that assortment are really just Easter Eggers with a designer label, using slightly different breeds as parents. It will be fun to see what color eggs you get, and if you have crests, miffs, beards, etc.
mine started laying between 19-22 weeks.
Their combs get pale any time they stop laying for an extended period of time, like when they are broody. So it could be the heat but also could be from being broody. I agree with the others to try to provide a wet mash to eat and other moisture rich foods.