As already discussed, a new process is created through fork() and if a new executable is to be run then exec() family of functions is called after fork(). As soon as this new process is created, it gets queued into the queue of processes that are ready to run.
If only fork() was called then it is highly likely that new process runs in user mode but if exec() is called then the new process will run in kernel mode until a fresh process address space is created for it.
While the process is running, a higher priority process can pre-empt it through an interrupt. In this case, the pre-empted process again goes into queue of processes that are ready to run. This process is picked up by the scheduler at some later stage.
A process can enter into kernel mode while running. This is possible when it requires access some resource like text file which is kept on hard disk. As operations involving access to hardware may take time, it is highly likely that process will go to sleep and will wake up only when the requested data is available. When the process is awakened, it does not mean that it will start executing immediately, it will again queue up and will be picked for execution by scheduler at appropriate time.
A process can be killed through many ways. It can call exit() function to exit or can process Linux signals to exit. Also, some signals cannot be caught and cause the process to terminate immediately.
There are different types of Linux process. Once the process is killed, it does not get completely eliminated. An entry containing some information related to it is kept in the Kernel process address table till the parent process explicitly calls wait() or waitpid() functions to get the exit status of child process. Until parent process does this, the terminated process is known as zombie process.
