Regarding why Chinese cash coins have square holes, the two responses you published are correct. The earliest cash coins, cast in the 300's and 200's BC, were made with round holes in some places and square holes in others. The square hole won out in order to file off the casting sprue.
Some numismatic works answer this question in cosmological terms -- the square hole represents the squareness of earth, with its four directions, while the round shape represents heaven, which is round (or more accurately hemi-spherical).
Howard A. Daniel III concurs. He writes:
Why do Chinese cash coins have holes? This question is not correct because it was not only the Chinese who issued cash coins! The Chinese issued the first one, but the Koreans, Japanese and Vietnamese also issued them, and the Vietnamese minted the last official cash coins. And there were many unofficial cash coins issued by merchants and mines and plantations in Southeast Asia too, and many unofficial coins had round center holes. So the question should be, "Why do official cash-style coins have square center holes?"
The square center hole in the coin represents the earth and the round outer shape represents the universe. With the king or emperor's reign title in two of the four characters on the obverse side, this showed the king or emperor was a supreme being.
The square center hole was also practical because a square rod was needed to hold the coin in place while excess metal was being filed off on those that needed it. And the holes in cash coins were also used to string them in groups of 500, 600 and/or 1000 when they were sent from the mint. And they often stayed strung to use to complete a transaction.
But a VERY important reason for the hole was that the great majority of East Asians did not have pockets in their clothes! For the upper classes, they had small coin bags, sacks or purses which were tied or looped on their belts to hold their coins, but the poorer people did have coin bags, sacks or purses and strung their coins on a string or wire and then put them on their wrist, belt or their carrying pole.
Thanks to everyone for their great responses on this topic. I'll file this with "Why are coins round?" as one of my favorite fundamental coin knowledge questions.