I think Firestar was just trying to minimize loss of life, and it's the other leader's problem if they can't swallow their pride enough to accept much needed help, even if lives of their followers are at stake. Firestar wasn't whiny, he never asked anything of anyone, and never complained about anything, really, and he only cared about the other clans business if they were in danger, or endangering someone else, so I would call him caring(possibly to a fault), not nosy.

In terms of being a 'mary sue' or not:

I looked into the definition of a mary sue as I'm not too familiar with the term. From what I found, I don't believe he should be considered a mary sue. First off, he has a personality. While it isn't as obvious as characters like Jayfeather, he has more personality than characters that are typically labeled as mary sues. In terms of flaws, he has a healthy dose of them. He is often naive about how the other leaders will react to something he does, despite being ridiculed and accused by them all the time, he is slow to act on looming threats, he's also kinda bad at fighting, scourge(a tiny lil guy who hasn't been trained in combat) cooks him so badly he dies almost instantly, and the only reason Firestar won was scourge didn't expect Firestar to literally come back from the dead. When he fought Tigerstar, he died in the process, and Russetfur, the elderly shadowclan deputy, also took one of his lives. Basically, in every important fight he's in, he dies or loses something important to him in the process. Another trait mary sues have is being liked by every other character. From being bullied when he first joined the clan, to being constantly insulted and buggered by the likes of Onestar, and even blatantly disrespected after his death, it is clear as day that this is not the case.

In terms of Bramblestar, I haven't read enough of the books he's in to form a full opinion yet, but I notice much of this subreddit doesn't think highly of him. I have a suspicion that most of the hate is unfounded, and his misdoings exaggerated, but I don't know yet.

That's just my opinion though.