What process state has when it calls a syscall?
I mean, don't asume it's an I/O syscall like read or write...
It's the process itselft that executes kernel code, or the process is suspendes and there's like a "kernel thread" that execute the syscall handler (and knows wich process called (current))?
I'm not sure if changes from executing to ready, or executing to blocked.
It's the process itself that switches to kernel mode and executes the system call - although it switches to a kernel stack to do so. A process executing inside the kernel has state Running, and can be pre-empted and end up in state Runnable.
It depends what the syscall does.
Suppose there is a hypothetical syscall which calculates PI to a lot of digits, and places the result in a buffer the application specifies, then the process will probably just be in the "R" running state. Switching to kernel mode doesn't stop it running in the context of the task that made the call.
Of course many system calls wait for things - consider sleep() for example, which releases the CPU rather than spinning. This puts the process to sleep, having registered a kernel timer to wake it up.
Quite a lot of syscalls never sleep, the likes of getpid() which just retrieve information which is always in ram. And many which do sometimes sleep don't necessarily do so, for example, if you call read() on data already in a kernel buffer.