[fluoridation]

Most of those are just phonetic approximations using convenient characters. I'm not sure I'd say the names have any semantic content. The names for China, Korea, and Japan are the names the ancient Chinese gave them. China is the "middle" or "center" country because it's the country of the people who named it. Japan is the origin of the sun because it's to the East of China. And of course the Han are what Koreans called themselves. Nothing accidental about any of those names.

[pimlottc]

Sure, but there are multiple characters nearly every sound in Mandarin, I’m sure it’s no accident they ended up with mostly flattering ones.

[pinkmuffinere]

+1, it's no accident. The most obvious case is with corporate names, which sometimes get carefully analyzed in translation. Coca-Cola is famously translated as 可口可乐 (Ke3 kou3 ke3 le4, numbers indicate tones), with individual characters meaning "can taste can happy", and intuitively meaning something like "drinkable deliciousness"

[0xis]

According to Baxter & Sagart (2014), the name Hán 韓 *[g]ˤar is from Gaya language word kara.

[Y_Y]

Indeed, that is what I wrote