*the number of seconds in most days
This is different from what happens in leap year, where February is actually lengthened and February 29 is considered a different day from February 28. It escapes me why leap seconds aren't treated that way. (I know, people say the stupid treatment of leap seconds is required by the POSIX definition of time. So what? Change the POSIX definition.)
i agree that this is a rather confusing way of putting it
No, it adds a 61th second to the last minute.
UNIX timestamps happen twice, because it's broken. NTP too.