If I am allowed to ramble on your post a bit I would like to throw my own two cents in on this. I would put it in the tags but it was getting too long . I will fully admit that I am 100% a subscriber to the fannon sentient 1010 headcannon, but I do think it has a bit more root in cannon if you take the repurposed warbots in Metro Division into consideration.
In Metro Division there is a post office that is overflowing with mail (assumed overflow because there are letters on the ground). When you interact with it, the flavor text mentions that the warbots have fake memories and they’re writing back to their non-existant families.
(Sorry if my pictures are blurry)
Sending home letters doesn’t serve any functional purpose to these warbots, so presumably there has to be an emotional drive to it (I can’t imagine it would be useful to program “get sentimental/sad and write home” into warbots meant to fight). Considering that the fake memories were to make them fight harder, it would make sense that emotions would only serve to make them fight even harder.
(Also based on Mayday’s dialogue, specifically “It doesn’t seem so sure by the end”, you could argue that maybe they’re starting to realize their memories are fake, which may imply sentience for being able to recognize that??? Or the start of gaining sentience??)
We also know that 1010 developed from MKI to MKIII, and the earliest, MKI, is in a more standard soldier uniform. Whether or not they actually served as warbots or were designed as such for theming purposes, they probably still shared a lot of the same initial components. It would make sense to recycle spare warbot parts and programs into new robots if they’d just be laying around otherwise.
So if 1010 are developed from/after warbots, they probably share a lot of the same hardware and software, meaning Neon J probably just modified the existing emotion software (assuming it exists) into something that can generate lovable stage personas. Due to this, I don’t think its unreasonable to assume 1010 has at least some emotion.
Additionally, emotion would probably go to make them a lot more likable by fans. Humans love human connection, so the more human those robots are, the more fans they might get.
Emotion of any extent would need complex programing, meaning it would be beneficial to have a cloud or central hub that they operate from/get backed up to. Assuming that these emotions develop and drive different patterns of behavior, changes to their AI (or whatever they run on), or other stuff that may affect how they act, losing a 1010 member would be a HUGE SETBACK. Not only would the new 1010 have to start over developing all those pathways again, they would probably develop differently than the previous one, which fans would probably not like. Like you said above, having that backup would also help them jump back into rhythm in battle considering how fast they get thrown back into it.
Most fannon stuff (including mine, lol) assumes that 1010 has sentience as well, which, if they have emotion, is probably not too far of a stretch in this fictional world of more advanced tech. They could then recognize that, assuming everything above is true, if their current body gets destroyed, they just go to a new one as the same person, explaining their nonchalance about being destroyed by B2J.
This backup process would also explain Neon J just throwing them at B2J without hesitation (also like you said). But when the factory is destroyed he tries to protect them. Because the factory is where 1010 comes back from when they’re destroyed, I assume that’s where their consciousness is backed up to. Without that factory, if their current 1010 bodies get destroyed, they’re gone, and NJ will have to start from scratch again. 1010 don’t realize that, which is why they don’t seem to care about being destroyed.
As far as how 1010 acted during the fight, considering how military Neon J is, I imagine that’s all strict protocol. On stage for actual performances or when interacting with fans they probably have some more freedom, but you need to be coordinated during a battle. Neon J has battle plans and they have to stick to them because this is a dangerous situation. I wouldn’t be surprised if all their dialogue at the start was scripted by Neon J himself. And during the fight, NJ’s barking commands the whole time that 1010 has a respond call for. Everything about that fight screams strictly rehearsed to me, they didn’t have a lot freedom to do anything else.
And who knows, maybe the fics are accurate. Almost being permanently killed by B2J may have triggered a lot emotions and maybe even the beginning of sentience development if they didn’t have it already.
tldr: Based on how the repurposed warbots write letters home, they likely have some emotion. Assuming 1010 was developed from the same kind of programming, 1010 probably has emotions as well, and maybe even sentience depending on how you view having emotions. Having a backup or cloud for 1010 would be beneficial so as not to lose the already existing personalities. When the factory was destroyed, this cloud or backup was also destroyed, hence Neon J trying to protect them. It’s still headcannon, but whole emotion and sentience thing is more supported in cannon than people may think.