First of all, I love the color of the baby. The color is certainly tricky and I don't have much experience with this particular color, but here is my "educated guess". Birmingham rollers come in as many colors as I can name probably so the options are wide open.
It will be easier to determine...
I don't have any experience with this particular model, but in general, I don't see anything wrong with most generic brand Chinese incubators. In my experience they usually work well. The thing is, that they are (more often than not) made with cheap and not very durable parts that can break down...
Well then I guess you need size 7, maybe 8 (less likely). Is there a band size number on the parent's bands? You could order your bands from the NPA, but they apparently only take orders of 50 bands and $20 minimum, and you don't need that many...
I wouldn't lose hope, they can still hatch... sometimes it can take over a day for them to hatch after the initial pip in the shell. There is not much you can do but wait at the moment.
Congrats on your baby pigeon!
I'm not sure what's the process where you come from, but here in Europe there are universal leg bands. They are made from plastic, there is a country tag on it, year of birth, size of leg band and a serial number so it's unique. We order them at our local...
Well, my guess is that there is some kind of a hole in the lid... For this system to work you need vacuum, and you can't have that if there's air coming in.
Well the egg in the pic looks good in my opinion.. I would turn them at least 3 times a day though... That is so they don't always spent the night on the same side (for example 9 am, 3 pm and 9 pm). Maybe the humidity is a bit too high (45-50 works best for me) but that depends on you climate...
Well brinsea incubators are usually good, the settings make sense and should be good. I have never done periodical cooling, which suppousedly helps, but I can't comment on that. Your eggs don't look like they started developing anyway, so this shouldn't have been a factor. The only thing that...
well it got darker because it was incubating, but I don't think there's any developent there... I candle my eggs with my phone's flashlight and it's pretty obvious which are fertile and which are not.
What settings did you use for the incubating?
Since it's day 15 my initial thought would be that they are not fertile. By now you should be able to see clear movement in the egg. With light color shell eggs like yours you should already see veins by day 5-6 and by day 7-8 there would be a clear web.
Are you sure there was a rooster with...
When I want to get into a new breed, I prefer to find a trustworthy breeder and buy an adult rooster and a couple of hens. That way I know what I'm getting and I can hatch good stock from a solid foundation. If that's not possible I'd order day old chicks from a reliable hatchery. Even if only...
I personally wouldn't hold my breath for any to hatch now, it's a real shame since they were so close...
That is why it's always a good idea to put a broody hen in a separate enclosed space so she doesn't even get tempted to get off the eggs. And if she does, you can always try to put a basket...
Here's a discussion about power outage solution that could actually work https://www.backyardchickens.com/t/371078/incubator-run-on-car-battery
3 hours of power outage shouldn't ruin the hatch and a temperature spike (if not too severe) also shouldn't do too much damage.
As far as the...