Regarding the first two footnotes, I’m pretty sure that originally the singular form “parenthesis” just refers to the aside inserted (by use of brackets, like this) into a sentence. Because it sounds like a plural and because of the expression “in parenthesis”, people probably mistakenly applied the word to the pair of symbols, and when that became common, started using the real plural “parentheses”. This has staying power because it’s fancy and “brackets” is way overloaded, but historically it’s probably just wrong and especially nonsensical in math and programming, where we don’t use them to insert little sidenotes.