hpzstatn.exe is installed the hardware drivers for your HP Digital Imaging solution. This is a non-essential process.
Disabling or enabling it is down to user preference.
Non-system processes like hpqcmon.exe originate from software you installed on your system. Since most applications store data in your system's registry, it is likely that your registry has suffered fragmentation and accumulated invalid entries which can affect your PC's performance. It is recommended that you check your registry to identify slowdown issues