I can't tell for sure from these pictures, but my guess is that these birds may not be BBs. Someone else with more experience may be able to be more definitive. It's hard to tell the body size of a tom when he's displaying, or the leg and breast size in any of these pictures, but on the first picture you've also included a chicken, which I'm guessing is a LF Americana (could be really wrong there). The tom appears to be reasonably mature in that picture based on head ornamentation, but he isn't HUGE compared to the chicken, which votes for heritage Bronze instead of BBB.
Also, you said these pictures are over a year old, so the birds must be at least 1 & 1/2 years old now, and they're still walking around. BBB tend to have significant leg problems long before that (although there are exceptions), and most don't even live that long. But yours are still trying to breed, so that's another vote for heritage Bronze.
Plus you said he flew to the top of the grill (OMG, so dangerous -- hope it wasn't hot at the time). BBB don't fly much, or perch much, except when very young. So another vote for heritage Bronze.
Do you know how much your son paid for these birds. Heritage Bronze tend to be more expensive. If you remember, or can look it up, call the store where they were purchased and ask which variety was most likely purchased at that price. If the person you speak with is no help, ask to speak to the manager.
As far as the lights, the reproductive cycle of the hen is regulated by something called photoperiod. That is the number of hours in a day that she is exposed to light vs dark. When the days start getting shorter, nature tells her that winter is coming, and when she is exposed to only a certain minimum threshold of light hours per day, she stops laying. When the number of hours of light starts to increase, then nature tells her that spring is coming, and when her brain detects a certain minimum threshold of light hours per day, she starts laying. If we interfere with that pattern by putting hens under artificial lights, then we can change their laying cycles. Many farmers with laying (chicken) hens do that intentionally to keep birds laying through the winter. Some breeds (of chickens) have been selected specifically for winter laying. But if you've had her under lights in the winter, that's why she laid all winter and is now stopped, because her TOTAL hours of light have now decreased because it's not so cold, and you've switched to a different kind of light that is probably lower intensity, so it doesn't affect her cycle, or at least affects it less. You've not injured her at all, but her pattern is just a little mixed up right now. If you want to provide a night light for them, the soft rose color is good, but make sure it is a very low wattage (4-10 watts is typical for a nightlight). It's not necessary, but can make it easier if you need to run out to their coop in the middle of the night, or if a bird falls off a roost and needs to get back up. (I'm not sure that's enough for a bird to see, but maybe it could help a little.) If you don't want her to lay all winter next year, then use a red heat lamp instead of a white lamp. It won't affect their cycle as much, probably not at all, and will allow them to sleep better. White heat lamps aren't recommended for poultry, for this and several other reasons.
when I candle the turkeys there is just a bit of fluid at the pointy end and the air cell still looks to be alittle behind... the goose eggs look to be a bit further along which makes sense as they were a touch higher.. Hopeful that it works out in the end.. holding off lockdown until I have an internal pip...
, I know they try to mate. But I didn't think they could. She has been known to be an egg eater. But since I have read some posts, I wonder if she is collecting a bunch. She a white hen. They are of unknown origin my son brought them home from 
I was just loving eating her eggs and now I can't find any. I read a post earlier that made me laugh, someone called them yard ornaments
