There's no need for threads. Set the pipe to non-blocking and ignore the write() error if it's EAGAIN/EWOULDBLOCK. See my response above for why dropping writes if a byte already exists in the pipe is okay.
(But yes, setting it non-blocking is correct.)
Perhaps but then you're mixing signals and threads and you're in for a whole new world of hurt. :)
E.g. I've found that OSX does not always behave correctly when delivering signals to a process where one thread has blocked the signal but another hasn't, though I cannot remember the exact details. And of course on any system there is such a thing as signals addressed to a specific thread rather than a whole process (ptherad_kill()).
I'm not really sure that thread-directed signals are in scope for the sorts of things where you must use signals (SIGINT, SIGTSTP, etc. from a terminal, SIGCHLD from child termination, etc.) Those should all be process-directed. If you design your own API that involves signals, then sure, but that's a problem of your own making.