Not always. The kill system call can be used to send any signal, it's just got a name that implies you're sending something like SIGKILL or SIGTERM. I have written C programs that use kill for harmless inter-process communication.
It's SIGINFO on the BSD's, and works with just about any process (though obviously not everything has a customized handler). Also handily mapped to Ctrl-T.
No because only SIGQUIT, SIGABRT, SIGKILL, SIGTERM and often SIGHUP are supposed to do that. All of the other signals have wildly varying meanings. See man 7 signal: http://unixhelp.ed.ac.uk/CGI/man-cgi?signal+7