In the legal sense, no. Unix is an operating system and has the components of an NOS (Network Operating System) but it not considered just a network operating system.
Many operating systems now can run on standalone computers and also on networked computers. Standalone or generic operating systems are the ones which run on standalone computers like Windows...
yes yes it is because the computer will say missing operating system without it and if the operating system is windows xp it will have a kernel named ntoskrnl.exe