Something else is I disagree here, Roxas absolute DID have a reason to ask about the keyblade. To Roxas the thing that had connected him and Xion, the thing that made them so similar, the thing that they shared with one another that no one in the organization else had was the keyblade. A point that was hammered in on him more than once and so you can see where his train of thought leads. "No one would tell me anything about her because she was a replica, a replica the organization made to use the keyblade....I can use the keyblade to and that's sort of our primary similarity does that mean this whole time I've been a replica as well? But wait there is something more than the keyblade connects us, Xemnas also said Sora connects us so who is Sora and what does he have to do with this?" It's a very clear organic line of thought and then it leads into Axel quickly clarifying to Roxas he wasn't a replica because that was a super off base thought. Which of course just makes Roxas even more antsy for answers because if Xion could use the keyblade because she is a replica, then what on earth is Roxas if he can use the keyblade but isn't a replica. Ultimately since no one gives him the answer he leaves the organization following the only clues he has, "sora".
Fittingly he gets Axel caught in crossfire, the obvious thing would be to explain to Roxas the truth about Sora but Axel believes Roxas will leave if he does that. Yet at the same time it's clear Roxas will leave if doesn't say anything so in theory Axel has nothing to lose....but the thing is it's easier for Axel as a person to lie than it is to tell the truth. Axel will lie at every chance he can get when he has the option, even if it's not necessary and even if it make things worse, because for Axel telling the truth is harder and unnatural. Axel is flat out a chronic liar and you know this is clearly an intended part of his character. Because a lot of chronic liars start out as children or teens who simply tell a small lie here or there regularly until it evolves into a way of life they can't break out of. They made sure in BBS to show this, that Lea would rather have Isa lie to him about the reality of losing his bout against Ventus and also was subtly denying the reality that Ventus beat him asking him to "call it a draw". These are friendly little gestures which alone don't mean much but they were a symptom of a much bigger problem that would snowball from this. Lea's views now would eventually lead to Axel developing into a chronic liar.
Likewise I think you're missing the context of that Roxas and Axel parting scene in the city. When Roxas says "no one would miss me" what he actually means is "No one I personally care about would miss me because there is no one left in the organization I feel for". His anger is fully justified in having learned that Axel lied to his face for pretty much his entire life, for all he knows most of the lessons he taught by Axel were lies. The fact is that Roxas simply can not trust Axel anymore, he gave Axel one last chance to be a good friend and tell him the truth....correction practically begged him but Axel turned him down. That's why the following scene is Roxas in his room talking about how he tried but there is nothing left keeping him at the organization anymore. He also has an interesting line of foreshadowing inserted just a bit earlier as he leaves the room with Axel saying that "somewhere out there is someone who will tell me the truth and that is the person I will trust". It foreshadows in the future his meeting with his sorta-half-sister Namine and how because she is doing something no one else did, tell him the truth, he latches onto her like a lost puppy and drinks in every word she says.
But really you have to think of the full ramifications of what Roxas learning Axel has been telling constant lies to him means. Most of his information and understanding of the world comes from Axel and now he's realizing that literally almost everything he knows in life could be nothing but a series of lies Axel told him. That Axel may of simply told him whatever he needed to mold Roxas into the person he wanted Roxas to be for him, that Axel may never have actually cared about his well being at all. Which is fair, Axel had a disgustingly large amount of power over Roxas's world and he abused it majorly. The realization has rightfully horrified Roxas and the fact remains Axel spurred that chance Roxas gave him to set things right. But I wouldn't call this any sort of temper tantrum, that's disrespectful to the graveness of this. He's not fuming over a lost toy he is literally realizing both how much he has been depending on others (specifically Axel) and how literally everyone he depended on has done nothing but lie to him no matter if they were friend or foe. So he tries to strike out for his answers on his own, Axel and Xion did so why can't he? And the answer is that Roxas was always so dependant on his friends or the organization that Roxas doesn't know HOW. Which is sort of the crux of causing Roxas to become the character we see (well that and DiZ inserting a new life into him, which mind you is why Days was never going to line up perfectly since the Roxas we see in Days is a Roxas who has memories of an entire regular life cycle on top of his own real ones) and why even in KH2 Roxas is still dependant it's just in that game he's dependant on Namine and HPO.
And of course Roxas slips back into mopping, anger doesn't last long no matter how white hot it eventually cools and Roxas had a full day to cool down and realize he has literally no where to go and no idea how to find this "sora". He acted entirely out of anger and now he realized that his anger adrenaline had blinded him to the reality, a reality that is only just now sinking in. So of course he's gone to the one place he knows he can always come back to, and of course he's huddled up basically ready to cry. He basically just had everything he ever knew come crashing down, suffered from a huge rush of anger, and now that it's faded he's just left more empty and alone than ever.
So I find Days is an overwhelming success connecting the Roxas we know from that game with the Roxas we know in KH2, and lining up with the cutscenes about him.
Also uh just throwing it out there but when you talk about Pandora gear and how it gives Donald and Goofy the organization weapons...you wrote that Donald gets the shield of Vexen's and Goofy gets the magic staff
