If I have a handle of a process and that process has stopped, Do I need to close the handle?
Can I use the handle to rerun the process?
Can I use the handle to find out information about the process?
Process handles are a Windows concept so as far a Unix and Linux are concerned, there is nothing to close in the first place. The parent process must however properly get the process exit status with waitpid or wait.
When a process has stopped, i.e. is suspended but has not exited, it can be resumed and you can find a lot of information about it.
When it has exited, there is nothing you can do to revive it or to get information about it (outside its exit status if not retrieved by its parent process).