I personally don’t like that coop, it was not designed with chickens in mind. Very few premade coops are. People use them successfully and with three chickens in your climate you should be OK, especially once you get the run built. I can certainly understand life and weather getting in the way of finishing it, but at 5 weeks you are not in a desperate hurry. They will be OK in just the coop section for a while.
Having three nests isn’t a problem, it’s just a waste. One nest would be sufficient for you, though I believe in flexibility so two isn’t bad. To me, three nests on a coop that size just shows they don’t know what they are doing. The roosts are lower than the nests. That greatly increases the possibility they will sleep in the nests instead of on the roosts. It’s something you will have to wait and see on. This type of thing does not come with guarantees but a lot of people have problems with that. But some don’t. I wish you luck.
Ventilation is not that good. If you open both those slides it isn’t horrible but I’m a firm believer in the more ventilation you have the better, as long as it does not create a breeze blowing on them in the winter. I checked your weather forecast in Paradise and see that you are forecast for lows slightly below freezing in the next few days. That’s not bad since they are feathered.
I don’t know how dark or cold it actually gets in your garage. As long as you can safely run electricity to that electric hen, you don’t need to be in the garage though it looks like you might have some rain coming so be careful with electricity in wet conditions. There are always complicating issues. Even outside in those temperatures with them 5 weeks old they probably don’t need the electric hen but it won’t hurt. For your peace of mind if nothing else you probably should use it. There is value in you not worrying.
If that garage has windows and reasonable daylight, I would not add any lights to the coop. Open those sliding vents and leave them open day and night. Ventilation will help day and night, not just during the day. Your roosts are well below those vents so any breeze will go over their heads. They probably won’t be sleeping on the roosts any way for the next several weeks, they will probably sleep on the floor. In your garage there should not be any breezes, outside any should go over their heads.
If the garage is kind of dark during the day, I’d probably put a light on a timer to mimic daylight, probably outside the coop so it shines in through a vent. If you move it outside, just leave those vents open and depend on natural light.
I’ve had chicks go through nights with lows in the mid 20’s, close to what is forecast for you, when the chicks were 5-1/2 weeks old. The unheated grow-out coop they were in had good wind protection on the floor where they were and a lot of good ventilation up high. My chicks had been raised outside in a large brooder in the coop with only one end heated. The other end cooled of a lot, sometimes there was even ice in it. The chicks spent some time in the colder section, some in the warm, so they were acclimated, I think that helps. To me the simplest way to acclimate them is to move the coop outside with the electric hen. They will play in the coop and go warm up when and if they need to. You can move them in and out, that works too, but to me it’s more time consuming and requires hands on. I like passive systems that work whether I do or not.
Good luck!