Is saying 'who cares' rude or maybe even disrespectful?
Solution 1:
The statement "Who cares?" is often seen as extremely rude and even arrogant. Let's look at a more specific case: consider George W. Bush's response to journalist Bill Hangley at a press event in 2001:
Because I had serious misgivings about the president’s performance to that point, my own involvement in the whole operation had left me feeling a bit like a pseudo person, so when I had the chance to shake Bush’s hand, I said, “Mr. President, I hope you only serve one term. I’m very disappointed in your work so far.”
His smiling response was swift: “Who cares what you think?”
This is a very small thing for a man in a position of importance to say. Although Hangley had criticized the president to his face, a man who was more sure of himself might have replied generously, even magnanimously: "I'm sorry you feel that way," perhaps, or "I am doing my best to change your mind." That sort of thing. Instead, what came out was rude to the point of arrogance. It is the statement of someone in power to someone who is powerless.
Granted, "Who cares what you think?" is more specific and pointed, but the general "Who cares?" amounts to the same thing.
But the statement is not always rude. It may also be a weak response to an accusation:
A: You know smoking will kill you, right? Yet you do it anyway.
B: Who cares? We all have to die of something.
That usage suggests a forced insouciance, a resignation in the face of the perceived powerlessness of the person to quit smoking.
It can also be triumphant and expansive, even exultant in a way that is not at all rude:
A: The weather report is saying heavy snow is expected next week.
B: Who cares? You and I will be at the conference in Hawaii that week!
Solution 2:
It is commonly used in everyday conversation, and in most uses it is disrespectful to somebody (not necessarily the person spoken to).
Solution 3:
In the simulated conversations the person saying "Who cares?" is doing so to dismiss an otherwise legitimate criticism that the second person is offering. This is in itself impolite or boorish. Since the conversations appear to be between intimates, the use of the phrase "Who cares?" is not in itself a sign of impoliteness. In formal encounters, however, it is to be avoided.
Solution 4:
"Who cares?" means rhetorically "It doesn't matter". It is more informal than the latter.
In your first example, The speaker who uses it is trying to say that the particular number doesn't matter because it is so much smaller than the what it is being compared to that it is negligeable.
In the second example, the speaker is trying to say that his nose-picking doesn't affect anybody.
Pragmatically, the phrase is short in the direction of being rude, but is not nearly in the 'slappable' scale. It is not ignorant to use, but because of its informality, might be considered an unthought-out reaction. In both examples, a more thoughtful response would be less confrontational. "Booger-picking doesn't compromise the health of other people, so I'd prefer to save time and effort by doing it here and now".
The distinction I'm trying to draw is that one might say "I am terribly sick" and if the response is "It doesn't matter", then that would be considered pretty rude.
In the end though, "who cares?" is often used confrontationally. It is nowhere near as rude as an epithet, and can be just as rude as a statement of facts. Hoever, you are right that there is some bit of negative affect to the usage.