Question

I have to know if a thread is currently executing a system call (e.g. read/write/etc.) by knowing its tid. Is there a way to do that in Linux?

Answer 1

This should list the state code of the thread

ps -p<pid> -o stat

The two relevant codes are:

D    uninterruptible sleep (usually IO)
S    interruptible sleep (waiting for an event to complete)

Edit:
If you want to get the exact system call programmatically, you could use ptrace as you have suggested and read EAX, you should also use the PTRACE_SYSCALL flag to have the process stop at the next system call entry.