From what I've googled, a signal may be handled by a random thread. And when that signal's handler is executing, it's temporarily blocked until handler returns.
QUESTION: Multiple signals of different types reached simultaneously. Do their handler execute simultaneously on multiple thread or all of them go to one randomly picked thread (SUB-QUESTION: in this case a handler could interrupt another handler's execution started previously, so there could be a interrupt stack?) ? Or mixed? For instance there are 3 type of signals received but only 2 thread free (this is actually the first case).
EXAMPLE: SIGHUP, SIGINT, SIGTERM reached almost simultaneously. The program has two available thread to dispatch signal handler execution.
SIDE-QUESTION: If signal handlers run in parallel, I'll have to use mutex to synchronize them properly. Otherwise 'volatile sig_atomic_t' would be enough, right?
Expected: all signals go to one thread (randomly picked) despite of their different signal types, I haven't seen an example of using mutexes and atoms to synchronize signal handlers.
Your understanding is correct - unless a signal was directed to a specific thread, there's no guarantee which thread will handle a signal. See POSIX's Signal Generation and Delivery and pthreads(7):
POSIX.1 distinguishes the notions of signals that are directed to the process as a whole and signals that are directed to individual threads. According to POSIX.1, a process-directed signal (sent using kill(2), for example) should be handled by a single, arbitrarily selected thread within the process.
So it may be delivered & handled by the same thread that's currently handling another signal (in that case, the previous handler may be interrupted by the new signal). Or may be delivered to another signal.
You can block other signals while one is being handled using sa_mask field
of sigaction to avoid a signal handler being interrupted.
SIDE-QUESTION: If signal handlers run in parallel, I'll have to use mutex to synchronize them properly. Otherwise 'volatile sig_atomic_t' would be enough, right?
You almost certainly don't want to use mutex in a signal handler. There are only few functions that can be safely called from a signal handler (you can only call the functions that are async-signal-safe). See signal-safty for more information.
If you can use volatile sig_atomic_t for whatever the purpose (do you need to co-ordinate execution of different signal handlers?), it should be preferred.
Expected: all signals go to one thread (randomly picked) despite of their different signal types, I haven't seen an example of using mutexes and atoms to synchronize signal handlers.
This is commonly done by blocking signals that you're interested in from main and fetching/handling them in a specific thread. See pthread_sigmask which also has an example on how to implement this.