For example, would 彼と私 always sound just as natural as 私と彼? Or is one preferred over the other for certain uses? And this would apply to any other name or pronoun besides 彼.
If I understand correctly, English speakers are trained to always say "(and) I" last for politeness. However, Japanese has no such rules. 彼と私 and 私と彼 are equally natural, and no one would care about the order even in formal settings. The same is true with 僕と君 vs 君と僕, あなたと私 vs 私とあなた, 私と社長 vs 社長と私, and so on. Whichever is fine.