A "router operating system" is called firmware. It runs a router. A regular OS (Operating System) runs your computer. Operating systems are provided by many different organizations and corporations. Firmware is provided by the manufacturer.
That depends entirely on what Operating System the router is running
Windows is the most best operating system
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remote server
It's a router. It is operating system independent.
different language, different hardware requirements
Between a Router and a computer they have CPU'S, RAM, ROM, and an Operating System. Those are the only things that a Router and a Computer have in common.
user exec mode
explain the different components of operating system in details
You have not indicated WHAT you want to "Restore": operating system? router?
difference between operating system and system software?
Normally, no. The router setup is usually contained within the device itself, so the operating system should not change anything.