Where do you live? Curious bc most people do not heat their coop, unless they are located in very cold areas with long periods of sustained cold, and even then most people don't heat their coop, they instead get cold-hardy breeds. Also, heaters often will draw a fair amount of energy. Perhaps a panel heater meant for use in coops (usually attached to a wall, next to a roost) may be a low power and safe heating solution.
With regards to lighting, that should be pretty easy bc you can light your coop with LED Christmas lights, which should draw only a small amount of energy. You'll want a timer so that the lights turn on/off at same time every day, and you can Lengthen their day using the time too.
We use a heat lamp connected to a thermostat, so it does not turn on unless temp in coop (at roost level) gets below 15F. It only raises the temp to around 0F when the outside temps are -17F. The one issue you want to avoid with any heating is to not get the coop warm so that they birds are shocked by the cold or will struggle if the heater dies or panels no longer work (or the electricity goes out when using a plug in system).
We light our coop, using a single bulb. It is connected to a timer, so we try to keep them at 14 hours light per day. You'll need to begin using light in September to avoid a slowdown in egg production. Some people on BYC are very opinionated against supplemental lighting bc they fear that the birds need a break. However, they will take a break (irregardless of supplemental lighting) when they molt. Since I have heritage breeds, they are not high production anyway, and I still get a lower rate of egg production in the winter when using supplemental lighting, but I still get eggs.
We do not use solar power, as our coop has proper electric (no extension cords). However, I think using solar for the supplemental lighting will be easy. The heating might be harder bc of the potentially higher energy requirements.
Good luck to you.
